Question

if $\triangle xyz \sim \triangle rst$ and $rs = 9$, $xy = 12$, and $yz = 20$, then what does $st$ equal? (1 point) \bigcirc 24 inches \bigcirc 17.5 inches \bigcirc 40 inches \bigcirc 15 inches

Explanation:

Step1: Recall similar triangles property

For similar triangles \(\triangle XYZ \sim \triangle RST\), the corresponding sides are proportional. So, \(\frac{XY}{RS}=\frac{YZ}{ST}\).

Step2: Substitute known values

We know \(XY = 12\), \(RS = 9\), and \(YZ = 20\). Substituting these into the proportion: \(\frac{12}{9}=\frac{20}{ST}\).

Step3: Solve for \(ST\)

Cross - multiply: \(12\times ST=9\times20\).
Simplify the right - hand side: \(12\times ST = 180\).
Then, \(ST=\frac{180}{12}\).
Calculate \(\frac{180}{12}=15\).

Answer:

15 inches