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

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 that:
- \( QS = 30 \)
- \( RT = 16 \)

Since the diagonals bisect each other, we can find the lengths of segments \( QU \) and \( RU \):

\[
QU = \frac{QS}{2} = \frac{30}{2} = 15
\]
\[
RU = \frac{RT}{2} = \frac{16}{2} = 8
\]

Now, we can use the Pythagorean theorem to find the length of one side of the rhombus (let's call it \( s \)).

In triangle \( QUR \):

\[
s^2 = QU^2 + RU^2
\]

Substituting the values:

\[
s^2 = 15^2 + 8^2
\]
\[
s^2 = 225 + 64
\]
\[
s^2 = 289
\]
\[
s = \sqrt{289} = 17
\]

Thus, the length of one of the sides of the rhombus is \( \boxed{17} \).