Question

in the figure below, △abc is similar to △xyz. what is the length of zx? enter only the number as an integer or decimal.

Explanation:

Step1: Find the similarity ratio

Since $\triangle ABC\sim\triangle XYZ$, the ratio of corresponding sides is the same. We can find the ratio using the sides $AB$ and $XY$. The ratio $k=\frac{XY}{AB}=\frac{7}{2}$.

Step2: Calculate the length of $ZX$

We know that the side $AC = 3$ corresponds to $ZX$. Using the similarity - ratio, we have $ZX=AC\times k$. Substituting the values, $ZX = 3\times\frac{7}{2}=\frac{21}{2}=10.5$.

Answer:

10.5