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 which answer is correct and why

46
46

14
14

34
34

17
17

Answer 1

To find the length of one side of the rhombus QRST, we can use the properties of the rhombus and its diagonals.

1. In any rhombus, the diagonals bisect each other at right angles. Therefore, if we have diagonals QS and RT, their intersection point U divides them into the following lengths:

   • QU = QS / 2 = 30 / 2 = 15
   • RU = RT / 2 = 16 / 2 = 8

2. Now we can use the Pythagorean theorem to compute the length of one side of the rhombus. In triangle QUR, we have:

   • QU = 15
   • RU = 8

Thus, we can find the length of side QR:

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

Therefore, the length of one side of the rhombus is 17.

The correct answer is 17.