Question

in the diagram below, \\( \triangle nop \sim \triangle lom \\). find \\( p \\).

write your answer as a whole number or a decimal. do not round.

\\( p = \\) meters

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle NOP\sim\triangle LOM\), the ratios of corresponding sides are equal. That is \(\frac{NO}{LO}=\frac{NP}{LM}\).

Step2: Substitute the known values

We know \(NO = 66\) m, \(NP=75\) m, \(LM = 100\) m, and \(LO=p\). Substituting into the proportion \(\frac{66}{p}=\frac{75}{100}\).

Step3: Cross - multiply

Cross - multiplying gives \(75p=66\times100\).

Step4: Solve for \(p\)

\(p=\frac{66\times100}{75}\).

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Answer:

\(p = 88\) meters