Question

1. △efg ~ △abc. find the value of x.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle EFG\sim\triangle ABC\), the ratios of corresponding sides are equal. So, \(\frac{FG}{BC}=\frac{FE}{BA}\).

Step2: Substitute the given values

We know \(FG = 36\), \(BC=9\), \(FE=x + 7\), and \(BA = 5\). Substituting these into the proportion \(\frac{36}{9}=\frac{x + 7}{5}\).

Step3: Simplify the left - hand side of the equation

\(\frac{36}{9}=4\), so the equation becomes \(4=\frac{x + 7}{5}\).

Step4: Solve for \(x\)

Multiply both sides of the equation by \(5\): \(4\times5=x + 7\), which is \(20=x + 7\). Then subtract \(7\) from both sides: \(x=20 - 7\).

Answer:

\(x = 13\)