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Using Properties of Similar Triangles to Solve for Sides

ΔABC is similar to ΔXYZ. AC = 5, BC = 3, XZ = 7.5 and ∠C = ∠Z = 90°. What is the lengt of side XZ?

$\overline{AC}\cong\overline{XZ},\ \overline{BC}\cong\overline{YZ}$

$\frac{\overline{AC}}{\overline{BC}}=\frac{\overline{XZ}}{\overline{YZ}}$

$\frac{5}{3}=\frac{?}{7.5}$

$5(7.5)=3(?)$

$\frac{37.5}{3}=\frac{3(?)}{3}$

$?=\overline{XZ}=12.5$