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 use your mental math

46
46

14
14

34
34

17
17

Answer 1

To find the length of one side of rhombus QRST, we can use the properties of rhombuses. The diagonals of a rhombus bisect each other at right angles.

Given that:

• \(QS = 30\), which means each half (from U to Q or U to S) is \(15\).
• \(RT = 16\), meaning each half (from U to R or U to T) is \(8\).

Now, we can form a right triangle using half of each diagonal:

• One leg of the triangle is \(15\) (half of \(QS\)).
• The other leg is \(8\) (half of \(RT\)).

We can use the Pythagorean theorem to find the length of the side \(s\) of the rhombus: \[ s^2 = 15^2 + 8^2 \] \[ s^2 = 225 + 64 \] \[ s^2 = 289 \] \[ s = \sqrt{289} = 17 \]

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