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A rectangle is formed from two right triangles. The base of the rectangle measures 80 yards and is labeled Johnson Avenue. The top of the rectangle is labeled Edison Avenue. The left side joining both the avenues is labeled 41st street and measures 60 yards. The right side of the rectangle is labeled 42nd street. A bank is located at the vertex of 41st street and Edison Avenue. The hypotenuse joining the bank and the vertex of Johnson Avenue and 42nd street is labeled park.
Sylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41st Street and Edison Avenue. Her house is at the corner of 42nd Street and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st Street, or she can walk through the park. The distance from 42nd Street to 41st Street is 80 yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90° angles, how much shorter is it for Sylvia to walk through the park?
(1 point)
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be BLANK
yards shorter.
Use the Pythagorean Theorem Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
Use the image to answer the question.
A rectangle is formed from two right triangles. The base of the rectangle measures 80 yards and is labeled Johnson Avenue. The top of the rectangle is labeled Edison Avenue. The left side joining both the avenues is labeled 41st street and measures 60 yards. The right side of the rectangle is labeled 42nd street. A bank is located at the vertex of 41st street and Edison Avenue. The hypotenuse joining the bank and the vertex of Johnson Avenue and 42nd street is labeled park.
Sylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41st Street and Edison Avenue. Her house is at the corner of 42nd Street and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st Street, or she can walk through the park. The distance from 42nd Street to 41st Street is 80 yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90° angles, how much shorter is it for Sylvia to walk through the park?
(1 point)
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be BLANK
yards shorter.
Answers
Answer
wrong
Answer
thats wrong agin
Answer
wrong its not 100 or 20 yards
Answer
finely thats wright
Answer
Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point)
this is the given triangle its a right trangle on the shorter side its 20 and on the longer side its 30
this is the given triangle its a right trangle on the shorter side its 20 and on the longer side its 30
Answered by
GPT 3.5
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be 100 yards shorter.
Answered by
GPT 3.5
I apologize for the incorrect response. Let's calculate the correct answer.
We can use the Pythagorean theorem to find the length of the hypotenuse joining the bank and the vertex of Johnson Avenue and 42nd street.
From the given information, the length of the base (Johnson Avenue) is 80 yards and the length of the left side (41st street) is 60 yards.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the length of the hypotenuse.
c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000
Taking the square root of both sides:
c = √10000
c = 100 yards
Therefore, the distance from the corner of 42nd Street and Johnson Avenue to the corner of 41st Street and Edison Avenue (walking through the park) is 100 yards.
Since the distance from 42nd Street to 41st Street is also 80 yards straight down Johnson Avenue, the difference in distance by walking through the park is:
80 yards - 100 yards = -20 yards
So, it is 20 yards shorter for Sylvia to walk through the park.
We can use the Pythagorean theorem to find the length of the hypotenuse joining the bank and the vertex of Johnson Avenue and 42nd street.
From the given information, the length of the base (Johnson Avenue) is 80 yards and the length of the left side (41st street) is 60 yards.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the length of the hypotenuse.
c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000
Taking the square root of both sides:
c = √10000
c = 100 yards
Therefore, the distance from the corner of 42nd Street and Johnson Avenue to the corner of 41st Street and Edison Avenue (walking through the park) is 100 yards.
Since the distance from 42nd Street to 41st Street is also 80 yards straight down Johnson Avenue, the difference in distance by walking through the park is:
80 yards - 100 yards = -20 yards
So, it is 20 yards shorter for Sylvia to walk through the park.
Answered by
GPT 3.5
I apologize for the mistake.
To find the difference in distance, we need to calculate the lengths of the two different paths.
Path 1: Walking straight down Johnson Avenue and then turning right on 41st Street.
Path 2: Walking through the park.
Path 1:
The length of the base (Johnson Avenue) is 80 yards.
The length of the left side (41st Street) is 60 yards.
Using the Pythagorean theorem:
Distance = √(80^2 + 60^2) = √(6400 + 3600) = √10000 = 100 yards.
Path 2:
The length of the hypotenuse (park) joining the bank and the vertex of Johnson Avenue and 42nd street is 100 yards.
Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and 41st Street, the walk will be the same distance, which is 100 yards.
To find the difference in distance, we need to calculate the lengths of the two different paths.
Path 1: Walking straight down Johnson Avenue and then turning right on 41st Street.
Path 2: Walking through the park.
Path 1:
The length of the base (Johnson Avenue) is 80 yards.
The length of the left side (41st Street) is 60 yards.
Using the Pythagorean theorem:
Distance = √(80^2 + 60^2) = √(6400 + 3600) = √10000 = 100 yards.
Path 2:
The length of the hypotenuse (park) joining the bank and the vertex of Johnson Avenue and 42nd street is 100 yards.
Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and 41st Street, the walk will be the same distance, which is 100 yards.
Answered by
GPT 3.5
Apologies for the confusion earlier. Let's calculate the correct answer.
To find the difference in distance, we need to compare the lengths of the two paths: walking through the park and walking straight down Johnson Avenue and 41st Street.
The length of Johnson Avenue is 80 yards and the length of 41st Street is 60 yards.
Using the Pythagorean theorem, we can find the length of the hypotenuse (c) connecting the bank to the corner of Johnson Avenue and 42nd Street:
c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000
c = √10000
c = 100 yards
So, the length of the hypotenuse (park) is 100 yards.
To find the difference in distance, we subtract the length of walking straight down Johnson Avenue and 41st Street (80 + 60 = 140 yards) from the length of walking through the park (100 yards):
140 - 100 = 40 yards
Therefore, it is 40 yards shorter for Sylvia to walk through the park than to walk straight down Johnson Avenue and 41st Street.
To find the difference in distance, we need to compare the lengths of the two paths: walking through the park and walking straight down Johnson Avenue and 41st Street.
The length of Johnson Avenue is 80 yards and the length of 41st Street is 60 yards.
Using the Pythagorean theorem, we can find the length of the hypotenuse (c) connecting the bank to the corner of Johnson Avenue and 42nd Street:
c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000
c = √10000
c = 100 yards
So, the length of the hypotenuse (park) is 100 yards.
To find the difference in distance, we subtract the length of walking straight down Johnson Avenue and 41st Street (80 + 60 = 140 yards) from the length of walking through the park (100 yards):
140 - 100 = 40 yards
Therefore, it is 40 yards shorter for Sylvia to walk through the park than to walk straight down Johnson Avenue and 41st Street.
Answered by
GPT 3.5
I apologize for the earlier mistakes. Thank you for pointing out the error, and I'm glad we were able to find the correct answer in the end. If you have any more questions or need further assistance, feel free to ask.
Answered by
GPT 3.5
To find the unknown side length in the given right triangle, we can use the Pythagorean theorem.
Let's label the unknown side as "x".
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have the following information:
One leg of the triangle is 20.
The other leg (longer side) of the triangle is 30.
Using the Pythagorean theorem:
x^2 = 20^2 + 30^2
x^2 = 400 + 900
x^2 = 1300
Taking the square root of both sides:
x = √1300
Rounding to the nearest hundredth, we get:
x ≈ 36.06 yards
Therefore, the unknown side length in the given right triangle is approximately 36.06 yards.
Let's label the unknown side as "x".
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have the following information:
One leg of the triangle is 20.
The other leg (longer side) of the triangle is 30.
Using the Pythagorean theorem:
x^2 = 20^2 + 30^2
x^2 = 400 + 900
x^2 = 1300
Taking the square root of both sides:
x = √1300
Rounding to the nearest hundredth, we get:
x ≈ 36.06 yards
Therefore, the unknown side length in the given right triangle is approximately 36.06 yards.
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