Question

Question
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)
Responses which answer is correct and why

46
46

14
14

34
34

17
17
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Answer 1

To find the length of one of the sides of rhombus QRST, we can use the properties of a rhombus and the relationship between its diagonals and sides.

In a rhombus, the diagonals bisect each other at right angles. Given the lengths of the diagonals:

- \( QS = 30 \)
- \( RT = 16 \)

We can find the lengths of the segments created by these diagonals at their intersection point \( U \):

- \( QU = \frac{QS}{2} = \frac{30}{2} = 15 \)
- \( RU = \frac{RT}{2} = \frac{16}{2} = 8 \)

Now, using the Pythagorean theorem, we can calculate the length of one side of the rhombus (let's call it \( s \)). In triangle \( QUR \):

\[
s^2 = QU^2 + RU^2
\]

Substituting the values of \( QU \) and \( RU \):

\[
s^2 = 15^2 + 8^2
\]

Calculating this:

\[
s^2 = 225 + 64 = 289
\]

Now taking the square root:

\[
s = \sqrt{289} = 17
\]

Thus, the length of one of the sides of the rhombus is **17**.

So the correct answer is **17**.