Question

Rhombus QRST has diagonal lines QS and RT the intersect at U. If QS=30 and RT=16, what is the length of one of the sites of the rhombus

14
46
17
34

Answer 1

In a rhombus, the diagonals bisect each other at right angles. Therefore, we can use the lengths of the diagonals to find the sides of the rhombus.

Given:
- \( QS = 30 \) (diagonal)
- \( RT = 16 \) (diagonal)

First, we can find the half-lengths of the diagonals:
- \( QU = \frac{QS}{2} = \frac{30}{2} = 15 \)
- \( RU = \frac{RT}{2} = \frac{16}{2} = 8 \)

Now, we can apply the Pythagorean theorem to find the length of one side of the rhombus (let's call the side \( s \)):
\[
s^2 = QU^2 + RU^2
\]
\[
s^2 = 15^2 + 8^2
\]
\[
s^2 = 225 + 64
\]
\[
s^2 = 289
\]
\[
s = \sqrt{289}
\]
\[
s = 17
\]

Therefore, the length of one side of the rhombus is \( 17 \).