Question

In the trapezoid below, start overline, S, T, end overline ST is parallel to start overline, P, Q, end overline PQ ​ . If R, Q, equals, 36RQ=36, R, T, equals, 22, point, 5RT=22.5, P, R, equals, 24PR=24, and P, Q, equals, 32PQ=32, find the length of start overline, S, T, end overline ST . Figures are not necessarily drawn to scale. P

Answer 1

The length of
`\(ST\)` is
`\(24\)`.

In a trapezoid where
`\(ST\)` is parallel to
`\(PQ\)`, we can use similar triangles to find the length of
`\(ST\)`.

Given that
`\(RQ = 36\)`,
`\(RT = 22.5\)`,
`\(PR = 24\)`, and
`\(PQ = 32\)`, we can use the ratios of corresponding sides in similar triangles. Let x be the length of
`\(ST\)`.

`\[ (QR)/(PT) = (RQ)/(PR) \]`

Substitute the given values:

`\[ (36)/(x) = (36)/(24) \]`

Now, cross-multiply to solve for x:

`\[ 36 * 24 = 36 * x \]`

`\[ x = (36 * 24)/(36) \]`

`\[ x = 24 \]`

So, the length of
`\(ST\)` is
`\(24\)`.

The below is the diagram of the question.