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 a b c or d which one is it and why

46
46

14
14

34
34

17

Answer 1

In a rhombus, the diagonals bisect each other at right angles. Given that \( QS = 30 \) and \( RT = 16 \), we can find half of each diagonal:

- Half of diagonal \( QS \):
\[
QU = \frac{QS}{2} = \frac{30}{2} = 15
\]

- Half of diagonal \( RT \):
\[
RU = \frac{RT}{2} = \frac{16}{2} = 8
\]

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

In triangle \( QUR \):
\[
QR^2 = QU^2 + RU^2
\]
Substituting the values we found:
\[
s^2 = 15^2 + 8^2
\]
\[
s^2 = 225 + 64
\]
\[
s^2 = 289
\]
\[
s = \sqrt{289} = 17
\]

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

The correct response is **d) 17**.