Question

in the diagram below, \\( \triangle onm\sim\triangle oqp \\). find c.
write your answer as a whole number or a decimal. do not round.

Explanation:

Step1: Use similarity of triangles property

Since \(\triangle ONM\sim\triangle OQP\), the ratios of corresponding sides are equal. That is \(\frac{ON}{OQ}=\frac{OM}{OP}\). Here, \(OM = 15\) yd, \(OP=20\) yd, \(ON = 12\) yd and \(OQ=c\).

Step2: Substitute values into the ratio

Substituting the values into \(\frac{ON}{OQ}=\frac{OM}{OP}\), we get \(\frac{12}{c}=\frac{15}{20}\).

Step3: Cross - multiply

Cross - multiplying gives \(15c=12\times20\).

Step4: Solve for \(c\)

First, calculate \(12\times20 = 240\). Then \(c=\frac{240}{15}\).

Answer:

\(16\)