Question

there are two similar triangles in the diagram. find the unknown measurement. x = □

Explanation:

Step1: Set up proportion

Since the two triangles are similar, the ratios of corresponding sides are equal. We have $\frac{40}{40 + 120}=\frac{20}{x}$.

Step2: Cross - multiply

$40x=20\times(40 + 120)$.

Step3: Simplify right - hand side

$40x=20\times160$, so $40x = 3200$.

Step4: Solve for x

$x=\frac{3200}{40}=80$.

Answer:

$80$