Question

Rhombus QRST has diagonal line 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?

Answer 1

In a rhombus, the diagonals bisect each other at right angles. Given the lengths of the diagonals, we can find the length of one side of the rhombus.

1. The lengths of the diagonals are given as:
- \( QS = 30 \)
- \( RT = 16 \)

2. Since the diagonals bisect each other at point \( U \), we can find the lengths of the half-diagonals:
- \( QU = \frac{QS}{2} = \frac{30}{2} = 15 \)
- \( RU = \frac{RT}{2} = \frac{16}{2} = 8 \)

3. Now, we can use the right triangle \( QUR \) to find the length of the side \( QR \) of the rhombus using the Pythagorean theorem:
\[
QR = \sqrt{QU^2 + RU^2}
\]
Substituting the values:
\[
QR = \sqrt{15^2 + 8^2}
\]
\[
QR = \sqrt{225 + 64}
\]
\[
QR = \sqrt{289}
\]
\[
QR = 17
\]

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