Question

in the figure below, (\triangle abc) is similar to (\triangle efg). what is the length of (overline{eg})? enter only the number. the solution is

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle EFG\), the ratios of corresponding sides are equal.

Step2: Set up the proportion

\(\frac{AC}{EG}=\frac{AB}{EF}\). We know \(AC = 5\), \(AB=3\), \(EF = 12\). Let \(EG=x\). Then \(\frac{5}{x}=\frac{3}{12}\).

Step3: Cross - multiply

\(3x=5\times12\).

Step4: Solve for \(x\)

\(3x = 60\), so \(x=\frac{60}{3}=20\).

Answer:

20