Question

in the figure below, △abc is similar to △xyz. what is the length of (overline{xy})? enter only the number as an integer or decimal. the solution is
figure of two triangles: △abc with ab=5, ac=8, bc=12; △xyz with xz=18, yz=27, xy unknown

Explanation:

Step1: Identify corresponding sides

Since $\triangle ABC \sim \triangle XYZ$, the ratios of corresponding sides are equal. So, $\frac{AB}{XY} = \frac{AC}{XZ} = \frac{BC}{YZ}$.
We have $AB = 5$, $AC = 8$, $XZ = 18$, $BC = 12$, $YZ = 27$. Let's use $\frac{AB}{XY} = \frac{AC}{XZ}$.

Step2: Set up the proportion

Substitute the known values: $\frac{5}{XY} = \frac{8}{18}$.

Step3: Solve for $XY$

Cross - multiply: $8\times XY = 5\times18$.
Calculate $5\times18 = 90$. So, $8XY = 90$.
Then, $XY=\frac{90}{8}=11.25$.

Answer:

11.25