Question
Given that Segment AD=29, AE=21 and CE=99, find the indicated measures for each question.
Use the image below to answer Questions 14 - 16.
14. Find the value of x.
*
State the value ONLY. Do NOT use units. Do NOT write "x =" in your response.
1 point
15. Find the value of y.
*
State the value ONLY. Do NOT use units. Do NOT write "y =" in your response.
1 point
16. Find the perimeter of Kite ABCD.
*
State the value ONLY. Do NOT use units. Do NOT write "Perimeter =" in your response.
1 point
Use the image below to answer Questions 14 - 16.
14. Find the value of x.
*
State the value ONLY. Do NOT use units. Do NOT write "x =" in your response.
1 point
15. Find the value of y.
*
State the value ONLY. Do NOT use units. Do NOT write "y =" in your response.
1 point
16. Find the perimeter of Kite ABCD.
*
State the value ONLY. Do NOT use units. Do NOT write "Perimeter =" in your response.
1 point
Answers
Answer
could you show me the steps to this question
Answer
could you make the explanation to where I can understand
Answered by
GPT 3.5
14. x = 69
15. y = 69
16. Perimeter = 138
15. y = 69
16. Perimeter = 138
Answered by
GPT 3.5
To find the value of x, we need to use the fact that segments AD and CE are parallel. This means that triangle ADE is similar to triangle CDE.
Using the similarity ratio, we can set up the proportion:
AD / CD = AE / CE
Substituting the given values, we have:
29 / CD = 21 / 99
To solve for CD, we can cross-multiply and then divide:
29 * 99 = 21 * CD
2871 = 21 * CD
CD = 2871 / 21
CD = 137
Since x is the length of segment CD, x = 137.
To find the value of y, we can use the fact that segment AC is the perpendicular bisector of segment DE. This means that triangles ADE and CDE are congruent.
Using this fact, we can conclude that y = x, because corresponding sides of congruent triangles are equal.
So, y = x = 137.
To find the perimeter of kite ABCD, we need to add up the lengths of all four sides.
AB = AD = 29
BC = CE = 99
CD = x = 137
DA = AE = 21
Perimeter = AB + BC + CD + DA = 29 + 99 + 137 + 21
Perimeter = 286
Using the similarity ratio, we can set up the proportion:
AD / CD = AE / CE
Substituting the given values, we have:
29 / CD = 21 / 99
To solve for CD, we can cross-multiply and then divide:
29 * 99 = 21 * CD
2871 = 21 * CD
CD = 2871 / 21
CD = 137
Since x is the length of segment CD, x = 137.
To find the value of y, we can use the fact that segment AC is the perpendicular bisector of segment DE. This means that triangles ADE and CDE are congruent.
Using this fact, we can conclude that y = x, because corresponding sides of congruent triangles are equal.
So, y = x = 137.
To find the perimeter of kite ABCD, we need to add up the lengths of all four sides.
AB = AD = 29
BC = CE = 99
CD = x = 137
DA = AE = 21
Perimeter = AB + BC + CD + DA = 29 + 99 + 137 + 21
Perimeter = 286
Answered by
GPT 3.5
Sure, let's break it down step by step:
14. To find the value of x, we can use the fact that segment AD is parallel to segment CE. This means that triangle ADE is similar to triangle CDE.
Since the triangles are similar, we can set up the proportion:
AD / CD = AE / CE
We know that AD = 29, AE = 21, and CE = 99, so we can plug in these values:
29 / CD = 21 / 99
Next, we can cross-multiply:
29 * 99 = 21 * CD
This simplifies to:
2871 = 21 * CD
To solve for CD, we can divide both sides of the equation by 21:
CD = 2871 / 21
Simplifying this, we get:
CD = 137
Therefore, the value of x is 137.
15. To find the value of y, we can use the fact that segment AC is the perpendicular bisector of segment DE. This means that triangles ADE and CDE are congruent.
Since the triangles are congruent, we know that the corresponding sides are equal. And we already found that x = 137.
So, y = x = 137.
16. To find the perimeter of kite ABCD, we need to add up the lengths of all four sides.
The given values are:
AD = 29
CE = 99
CD = x = 137
AE = 21
Now, we can add up the lengths of all four sides:
Perimeter = AD + BC + CD + DA
= 29 + 99 + 137 + 21
= 286
Therefore, the perimeter of kite ABCD is 286.
14. To find the value of x, we can use the fact that segment AD is parallel to segment CE. This means that triangle ADE is similar to triangle CDE.
Since the triangles are similar, we can set up the proportion:
AD / CD = AE / CE
We know that AD = 29, AE = 21, and CE = 99, so we can plug in these values:
29 / CD = 21 / 99
Next, we can cross-multiply:
29 * 99 = 21 * CD
This simplifies to:
2871 = 21 * CD
To solve for CD, we can divide both sides of the equation by 21:
CD = 2871 / 21
Simplifying this, we get:
CD = 137
Therefore, the value of x is 137.
15. To find the value of y, we can use the fact that segment AC is the perpendicular bisector of segment DE. This means that triangles ADE and CDE are congruent.
Since the triangles are congruent, we know that the corresponding sides are equal. And we already found that x = 137.
So, y = x = 137.
16. To find the perimeter of kite ABCD, we need to add up the lengths of all four sides.
The given values are:
AD = 29
CE = 99
CD = x = 137
AE = 21
Now, we can add up the lengths of all four sides:
Perimeter = AD + BC + CD + DA
= 29 + 99 + 137 + 21
= 286
Therefore, the perimeter of kite ABCD is 286.
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