Question

1. if △gfe ~ △cbe, find fe.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle GFE\sim\triangle CBE\), the ratios of corresponding sides are equal. That is \(\frac{FE}{BE}=\frac{GE}{CE}\).
Substitute the given expressions: \(\frac{4x - 1}{x + 5}=\frac{60}{24}\).

Step2: Simplify the right - hand side ratio

Simplify \(\frac{60}{24}=\frac{5}{2}\). So the equation becomes \(\frac{4x - 1}{x + 5}=\frac{5}{2}\).
Cross - multiply: \(2(4x - 1)=5(x + 5)\).

Step3: Expand and solve for \(x\)

Expand: \(8x-2 = 5x + 25\).
Subtract \(5x\) from both sides: \(8x-5x-2=5x-5x + 25\), \(3x-2=25\).
Add \(2\) to both sides: \(3x-2 + 2=25+2\), \(3x=27\).
Divide by \(3\): \(x = 9\).

Step4: Find the length of \(FE\)

Substitute \(x = 9\) into \(FE=4x - 1\).
\(FE=4\times9-1=36 - 1=35\).

Answer:

\(35\)