Question

hi || gj. find fh.
fh =

Explanation:

Step1: Apply the basic proportionality theorem (Thales' theorem)

Since \(HI\parallel GJ\), by the basic proportionality theorem, \(\frac{FG}{FH}=\frac{FJ}{FI}\). Let \(FH = x\), then \(FG=x - 36\) and \(FI=36 + 48=84\).

Step2: Substitute values into the proportion

We have \(\frac{x - 36}{x}=\frac{36}{84}\). Cross - multiply: \(84(x - 36)=36x\).

Step3: Expand and solve the equation

Expand \(84x-84\times36 = 36x\). Then \(84x-36x=84\times36\). \(48x = 84\times36\). \(x=\frac{84\times36}{48}\). Simplify \(\frac{84\times36}{48}=\frac{7\times12\times3\times12}{4\times12}=63\).

Answer:

\(63\)