Question

in the diagram below, $\triangle ihg \sim \triangle feg$. find $z$.

(diagram: right triangle feg with right angle at e, ef = 60 yd, fg = 68 yd. right triangle ihg with right angle at h, ig = 34 yd, ih = z. g is the intersection point of the hypotenuses.)

write your answer as a whole number or a decimal. do not round.

$z = \square$ yards

Explanation:

Step1: Identify Similar Triangles Ratio

Since $\triangle IHG \sim \triangle FEG$, the ratios of corresponding sides are equal. The ratio of $IG$ to $FG$ is $\frac{34}{68}=\frac{1}{2}$.

Step2: Apply Ratio to Corresponding Side

The side $IH$ (length $z$) corresponds to side $EF$ (length 60 yd). Using the similarity ratio $\frac{1}{2}$, we have $\frac{z}{60}=\frac{1}{2}$.

Step3: Solve for z

Multiply both sides by 60: $z = 60\times\frac{1}{2}=30$.

Answer:

30