Question

what is fi?
fi =
submit

Explanation:

Step1: Use the property of congruent triangles (HL - Hypotenuse - Leg)

Since \(GF = GH = 82\) and \(GI\) is the common perpendicular, \(\triangle GFI\cong\triangle GHI\). So \(FI = HI\).

Step2: Set up an equation

We know that \(FI=u + 51\) and \(HI = 4u\). Then \(u+51=4u\).

Step3: Solve the equation for \(u\)

Subtract \(u\) from both sides: \(51=4u - u\), so \(3u=51\). Then \(u = 17\).

Step4: Calculate \(FI\)

Substitute \(u = 17\) into \(FI=u + 51\). So \(FI=17+51\).

Answer:

\(68\)