Question
Rhombus QRST has diagonal lines QS¯¯¯¯¯¯¯ and RT¯¯¯¯¯¯¯ that intersect at U . If QS¯¯¯¯¯¯¯=30 and RT¯¯¯¯¯¯¯=16 , what is the length of one of the sides of the rhombus?(1 point)
Responses use your mental math
46
46
14
14
34
34
17
17
Responses use your mental math
46
46
14
14
34
34
17
17
Answers
Answered by
GPT-4o mini
To find the length of one side of rhombus QRST, we can use the properties of rhombuses. The diagonals of a rhombus bisect each other at right angles.
Given that:
- \(QS = 30\), which means each half (from U to Q or U to S) is \(15\).
- \(RT = 16\), meaning each half (from U to R or U to T) is \(8\).
Now, we can form a right triangle using half of each diagonal:
- One leg of the triangle is \(15\) (half of \(QS\)).
- The other leg is \(8\) (half of \(RT\)).
We can use the Pythagorean theorem to find the length of the side \(s\) of the rhombus:
\[
s^2 = 15^2 + 8^2
\]
\[
s^2 = 225 + 64
\]
\[
s^2 = 289
\]
\[
s = \sqrt{289} = 17
\]
Thus, the length of one side of the rhombus is **17**.
Given that:
- \(QS = 30\), which means each half (from U to Q or U to S) is \(15\).
- \(RT = 16\), meaning each half (from U to R or U to T) is \(8\).
Now, we can form a right triangle using half of each diagonal:
- One leg of the triangle is \(15\) (half of \(QS\)).
- The other leg is \(8\) (half of \(RT\)).
We can use the Pythagorean theorem to find the length of the side \(s\) of the rhombus:
\[
s^2 = 15^2 + 8^2
\]
\[
s^2 = 225 + 64
\]
\[
s^2 = 289
\]
\[
s = \sqrt{289} = 17
\]
Thus, the length of one side of the rhombus is **17**.
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