Question

if triangles ade and abc shown in the figure below are similar, what is the value of x? a 10 b 5 c 4 d 6 e 8

Explanation:

Step1: Find the ratio of corresponding sides

Since \(\triangle ADE\sim\triangle ABC\), the ratio of corresponding sides is \(\frac{AD}{AB}=\frac{2}{2 + 4}=\frac{2}{6}=\frac{1}{3}\)

Step2: Set up proportion for side \(x\)

We know that \(\frac{AD}{AB}=\frac{DE}{BC}\), substituting values \(\frac{1}{3}=\frac{x}{12}\)

Step3: Solve for \(x\)

Cross - multiply: \(3x=12\), then \(x = 4\)

Answer:

C. 4