Identify the whole-number measure of segment AD¯ that would create △ABD and △ACD as shown.
ABD has 4 and 8, ACD has 5 and 15
23 answers
To create △ABD and △ACD as shown, the whole-number measure of segment AD¯ should be equal to the sum of 4 and 5, which is 9.
the answer is greater than 9
Apologies for the incorrect response.
To create △ABD and △ACD as shown, the whole-number measure of segment AD¯ should be equal to the sum of 4 and 15, which is 19.
To create △ABD and △ACD as shown, the whole-number measure of segment AD¯ should be equal to the sum of 4 and 15, which is 19.
the answer is 11, but why??
I apologize for the confusion. To understand why the answer is 11, let's analyze the information given.
In triangle ABD, we are given that segment AB¯ has a measure of 4 units and segment BD¯ has a measure of 8 units.
In triangle ACD, we are given that segment AC¯ has a measure of 5 units and segment CD¯ has a measure of 15 units.
To create similar triangles, the ratios of corresponding sides must be equal. So, we can set up the following proportions:
AB¯/AD¯ = BD¯/CD¯
Substituting the given values:
4/AD¯ = 8/15
To solve for AD¯, we can cross multiply:
(4)(15) = (8)(AD¯)
60 = 8AD¯
Dividing both sides by 8 gives:
AD¯ = 7.5
Since we need a whole-number measure for AD¯, we round to the nearest whole number, which is 8.
Therefore, the whole-number measure of segment AD¯ that would create △ABD and △ACD is 8.
In triangle ABD, we are given that segment AB¯ has a measure of 4 units and segment BD¯ has a measure of 8 units.
In triangle ACD, we are given that segment AC¯ has a measure of 5 units and segment CD¯ has a measure of 15 units.
To create similar triangles, the ratios of corresponding sides must be equal. So, we can set up the following proportions:
AB¯/AD¯ = BD¯/CD¯
Substituting the given values:
4/AD¯ = 8/15
To solve for AD¯, we can cross multiply:
(4)(15) = (8)(AD¯)
60 = 8AD¯
Dividing both sides by 8 gives:
AD¯ = 7.5
Since we need a whole-number measure for AD¯, we round to the nearest whole number, which is 8.
Therefore, the whole-number measure of segment AD¯ that would create △ABD and △ACD is 8.
no AD is a verticle line inside a triangle that seperates ABD and ACD
Apologies for the misunderstanding.
If AD is a vertical line inside the triangle that separates ABD and ACD, we can determine the measure of AD¯ by looking at the proportions of the triangles.
In triangle ABD, AB¯ is given as 4 units and BD¯ is given as 8 units.
In triangle ACD, AC¯ is given as 5 units and CD¯ is given as 15 units.
Since AD¯ is the vertical line segment that separates these two triangles, AD¯ is the sum of AB¯ and BD¯, which is 4 + 8 = 12 units.
Therefore, the whole-number measure of segment AD¯ that would create △ABD and △ACD as shown is 12.
If AD is a vertical line inside the triangle that separates ABD and ACD, we can determine the measure of AD¯ by looking at the proportions of the triangles.
In triangle ABD, AB¯ is given as 4 units and BD¯ is given as 8 units.
In triangle ACD, AC¯ is given as 5 units and CD¯ is given as 15 units.
Since AD¯ is the vertical line segment that separates these two triangles, AD¯ is the sum of AB¯ and BD¯, which is 4 + 8 = 12 units.
Therefore, the whole-number measure of segment AD¯ that would create △ABD and △ACD as shown is 12.
why not 15-4?
I apologize for the confusion in my previous responses. You are correct that the measure of AD¯ can be found by subtracting the length of AB¯ from the length of CD¯, as AD¯ acts as the vertical line segment that separates triangles ABD and ACD.
In this case, if AB¯ has a measure of 4 units and CD¯ has a measure of 15 units, we can calculate the length of AD¯ by subtracting 4 from 15:
AD¯ = CD¯ - AB¯
= 15 - 4
= 11 units
Therefore, the whole-number measure of segment AD¯ that would create △ABD and △ACD as shown is 11. Thank you for pointing out the correct calculation.
In this case, if AB¯ has a measure of 4 units and CD¯ has a measure of 15 units, we can calculate the length of AD¯ by subtracting 4 from 15:
AD¯ = CD¯ - AB¯
= 15 - 4
= 11 units
Therefore, the whole-number measure of segment AD¯ that would create △ABD and △ACD as shown is 11. Thank you for pointing out the correct calculation.
The measure of two sides of a triangle are 7 and 11. Determine the range of values for the third side of the triangle.(1 point)
To determine the range of values for the third side of the triangle, we can use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's denote the third side as x. The given sides are 7 and 11.
So, we have the following condition:
x + 7 > 11 (sum of the known side and the third side must be greater than the other known side)
x > 11 - 7
x > 4
Thus, the third side of the triangle must be greater than 4.
In summary, the range of values for the third side of the triangle is x > 4.
Let's denote the third side as x. The given sides are 7 and 11.
So, we have the following condition:
x + 7 > 11 (sum of the known side and the third side must be greater than the other known side)
x > 11 - 7
x > 4
Thus, the third side of the triangle must be greater than 4.
In summary, the range of values for the third side of the triangle is x > 4.
the format for this question is blank<n<blank. do the answer that way
Apologies for the confusion.
Based on the triangle inequality theorem, the range of values for the third side of the triangle can be expressed as:
7 - 11 < x < 7 + 11
Simplifying the inequality:
-4 < x < 18
Therefore, the range of values for the third side of the triangle is -4 < x < 18.
Based on the triangle inequality theorem, the range of values for the third side of the triangle can be expressed as:
7 - 11 < x < 7 + 11
Simplifying the inequality:
-4 < x < 18
Therefore, the range of values for the third side of the triangle is -4 < x < 18.
its 4 not negative 4
Apologies for the error.
Based on the triangle inequality theorem, the range of values for the third side of the triangle can be expressed as:
11 - 7 < x < 11 + 7
Simplifying the inequality:
4 < x < 18
Therefore, the range of values for the third side of the triangle is 4 < x < 18.
Based on the triangle inequality theorem, the range of values for the third side of the triangle can be expressed as:
11 - 7 < x < 11 + 7
Simplifying the inequality:
4 < x < 18
Therefore, the range of values for the third side of the triangle is 4 < x < 18.
Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.
To determine the length of the third side of the triangle given that the first two sides measure 10 and 12, we can use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's denote the length of the third side as x. The given sides are 10 and 12.
Using the triangle inequality theorem, we can set up the following inequality:
10 + 12 > x
Simplifying the inequality:
22 > x
Therefore, the length of the third side of the triangle must be less than 22.
There is no specific range of values provided for the choices, so the length of the third side could be any value less than 22.
Let's denote the length of the third side as x. The given sides are 10 and 12.
Using the triangle inequality theorem, we can set up the following inequality:
10 + 12 > x
Simplifying the inequality:
22 > x
Therefore, the length of the third side of the triangle must be less than 22.
There is no specific range of values provided for the choices, so the length of the third side could be any value less than 22.
these are the options:
15
24
30
22
15
24
30
22
To determine the length of the third side of the triangle from the given options of 15, 24, 30, and 22, we need to find the option that satisfies the triangle inequality theorem.
According to the triangle inequality theorem, for a triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.
Given that the first two sides measure 10 and 12, we can compare their sum with each of the given options:
10 + 12 = 22
Comparing 22 with the given options, we find that the length of the third side must be equal to 22 in order to satisfy the triangle inequality theorem.
Therefore, the correct option is 22.
According to the triangle inequality theorem, for a triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.
Given that the first two sides measure 10 and 12, we can compare their sum with each of the given options:
10 + 12 = 22
Comparing 22 with the given options, we find that the length of the third side must be equal to 22 in order to satisfy the triangle inequality theorem.
Therefore, the correct option is 22.
but u said the option should be less than 22, not equal to or over
Apologies for the confusion in my previous response.
You are correct. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the first two sides measure 10 and 12, we can compare their sum with each of the given options:
10 + 12 = 22
Since the sum of the first two sides is 22, any option less than 22 would satisfy the triangle inequality theorem. Thus, the correct option is 15.
Therefore, the length of the third side of the triangle is 15.
You are correct. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the first two sides measure 10 and 12, we can compare their sum with each of the given options:
10 + 12 = 22
Since the sum of the first two sides is 22, any option less than 22 would satisfy the triangle inequality theorem. Thus, the correct option is 15.
Therefore, the length of the third side of the triangle is 15.
Two sides of a triangle measure 4 cm and 9 cm. Determine which of the following choices cannot be the measure of the third side.(1 point)
Responses
6 cm
6 cm
8 cm
8 cm
5 cm
5 cm
10 cm
Responses
6 cm
6 cm
8 cm
8 cm
5 cm
5 cm
10 cm
To determine which of the given choices cannot be the measure of the third side of the triangle, we can use the triangle inequality theorem.
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the first two sides measure 4 cm and 9 cm, we can compare their sum with each of the given choices:
4 + 9 = 13 cm
Comparing 13 cm with the given choices, we can assess whether the sum of the two sides is greater than the length of the given choice.
For the given choices:
- The sum of 4 cm and 6 cm is 10 cm, which is less than 13 cm.
- The sum of 4 cm and 8 cm is 12 cm, which is less than 13 cm.
- The sum of 4 cm and 5 cm is 9 cm, which is less than 13 cm.
- The sum of 4 cm and 10 cm is 14 cm, which is greater than 13 cm.
Therefore, the measure of the third side cannot be 10 cm.
Hence, the correct answer is 10 cm.
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the first two sides measure 4 cm and 9 cm, we can compare their sum with each of the given choices:
4 + 9 = 13 cm
Comparing 13 cm with the given choices, we can assess whether the sum of the two sides is greater than the length of the given choice.
For the given choices:
- The sum of 4 cm and 6 cm is 10 cm, which is less than 13 cm.
- The sum of 4 cm and 8 cm is 12 cm, which is less than 13 cm.
- The sum of 4 cm and 5 cm is 9 cm, which is less than 13 cm.
- The sum of 4 cm and 10 cm is 14 cm, which is greater than 13 cm.
Therefore, the measure of the third side cannot be 10 cm.
Hence, the correct answer is 10 cm.
1 answer