Question

1. if △gfe ~ △cbe, find fe.

Explanation:

Step1: Use property of similar triangles

Since $\triangle GFE\sim\triangle CBE$, the ratios of corresponding - sides are equal. That is, $\frac{FE}{BE}=\frac{GE}{CE}$.
We know that $FE = 4x - 1$, $BE=x + 5$, $GE = 60$, and $CE = 24$. So, $\frac{4x-1}{x + 5}=\frac{60}{24}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{4x-1}{x + 5}=\frac{60}{24}$ gives us $24(4x-1)=60(x + 5)$.
Expand both sides: $96x-24 = 60x+300$.

Step3: Solve for x

Subtract $60x$ from both sides: $96x-60x-24=60x-60x + 300$, which simplifies to $36x-24 = 300$.
Add 24 to both sides: $36x-24 + 24=300 + 24$, so $36x=324$.
Divide both sides by 36: $x=\frac{324}{36}=9$.

Step4: Find FE

Substitute $x = 9$ into the expression for $FE$. Since $FE = 4x-1$, then $FE=4\times9-1=36 - 1=35$.

Answer:

35