Question

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

Explanation:

Step1: Identify similar triangles' sides

The two similar triangles are \(\triangle OPQ\) and \(\triangle ORS\). The ratio of corresponding sides should be equal. The height of \(\triangle OPQ\) is \(60\), and the height of \(\triangle ORS\) is \(60 + 180=240\). The base of \(\triangle OPQ\) is \(20\), and the base of \(\triangle ORS\) is \(x\).

Step2: Set up proportion

Since the triangles are similar, \(\frac{60}{240}=\frac{20}{x}\) (ratio of heights = ratio of bases). Cross - multiply: \(60x = 240\times20\).

Step3: Solve for x

First, calculate \(240\times20 = 4800\). Then, \(x=\frac{4800}{60}\).

Answer:

\(80\)