Question

Question
Rhombus QRST
has diagonal lines QS¯¯¯¯¯¯¯
and RT¯¯¯¯¯¯¯
that intersect at U
. If QS¯¯¯¯¯¯¯=42
and RT¯¯¯¯¯¯¯=40
, what is the length of ST¯¯¯¯¯¯¯
?(1 point)
Responses

41
41

58
58

29
29

9
9
Remaining Attempts : 3
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page 4 of 4

Answer 1

In a rhombus, the diagonals bisect each other at right angles. This means that point U, where the diagonals intersect, is the midpoint of both diagonals.

Given that:
- Length of diagonal QS = 42
- Length of diagonal RT = 40

Since U is the midpoint of QS and RT:

1. The half-length of diagonal QS (QU or US):
\[
QU = \frac{QS}{2} = \frac{42}{2} = 21
\]

2. The half-length of diagonal RT (RU or UT):
\[
RU = \frac{RT}{2} = \frac{40}{2} = 20
\]

Now, in a rhombus, each side can be found by using the Pythagorean theorem. The sides of the rhombus are equal, and we can create a right triangle using half the lengths of the diagonals.

Let the length of each side of the rhombus (ST) be \( s \):
\[
s = \sqrt{(QU)^2 + (RU)^2}
\]
\[
s = \sqrt{21^2 + 20^2}
\]
\[
s = \sqrt{441 + 400}
\]
\[
s = \sqrt{841}
\]
\[
s = 29
\]

Therefore, the length of ST is **29**.

The correct answer is **29**.