Question

in the diagram below, △gfe ~ △dce. find z.
diagram with triangles: △dce has cd = 69 ft, ce = 48 ft; △gfe has gf = 46 ft, fe = z. the triangles intersect at e.
write your answer as a whole number or a decimal. do not round.
z = \boxed{} feet

Explanation:

Step1: Recall Similar Triangles Property

Since $\triangle GFE \sim \triangle DCE$, their corresponding sides are proportional. So, $\frac{GF}{DC} = \frac{FE}{CE}$.

Step2: Substitute Known Values

We know $GF = 46$ ft, $DC = 69$ ft, and $CE = 48$ ft, $FE = z$. Substituting these into the proportion: $\frac{46}{69} = \frac{z}{48}$.

Step3: Solve for \( z \)

Cross - multiply: $69z = 46\times48$. Then, $z=\frac{46\times48}{69}$. Simplify: $46$ and $69$ have a common factor of $23$ (since $46 = 23\times2$, $69 = 23\times3$), so $\frac{46}{69}=\frac{2}{3}$. Then $z=\frac{2\times48}{3}=32$.

Answer:

32