Question

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

46
46

14
14

34
34

17
17
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Answer 1

To find the length of one of the sides of rhombus QRST, we can use the property that the diagonals of a rhombus bisect each other at right angles.

Given:
- Diagonal QS = 30, so half of this diagonal (QU) = 30/2 = 15.
- Diagonal RT = 16, so half of this diagonal (RU) = 16/2 = 8.

Now, we form a right triangle QUU (where U is the intersection point of the diagonals).

Using the Pythagorean theorem:
\[
QR^2 = QU^2 + RU^2
\]
Substituting the values:
\[
QR^2 = 15^2 + 8^2
\]
\[
QR^2 = 225 + 64
\]
\[
QR^2 = 289
\]
Taking the square root:
\[
QR = \sqrt{289} = 17
\]

Therefore, the length of one of the sides of the rhombus is **17**.