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)

Question

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.