Question

what is fi? fi =

Explanation:

Step1: Use congruent - triangle property

Since $\angle FIH=\angle FGH = 90^{\circ}$ and $\angle FHI=\angle FHG = 48^{\circ}$ and $FH$ is common to $\triangle FIH$ and $\triangle FGH$, by the Angle - Angle - Side (AAS) congruence criterion, $\triangle FIH\cong\triangle FGH$. So, $FI = FG$.

Step2: Set up an equation

We know that $FI = 3w$ and $FG=w + 50$. Since $FI = FG$, we have the equation $3w=w + 50$.

Step3: Solve the equation for $w$

Subtract $w$ from both sides: $3w−w=w + 50−w$, which simplifies to $2w=50$. Then divide both sides by 2: $w=\frac{50}{2}=25$.

Step4: Find the length of $FI$

Substitute $w = 25$ into the expression for $FI$. Since $FI = 3w$, then $FI=3\times25 = 75$.

Answer:

75