Question

what is the value of x? enter your answer, as a decimal, in the box. ft

Explanation:

Step1: Identify similar - triangles

Since the lines are parallel, $\triangle NAB\sim\triangle NMP$.

Step2: Set up proportion

The ratio of corresponding sides of similar triangles is equal. So, $\frac{NA}{NM}=\frac{AB}{MP}$. Here, $NA = 22$ ft, $NM=71.5$ ft, and $MP = 97.5$ ft. Let $AB = x$. The proportion is $\frac{22}{71.5}=\frac{x}{97.5}$.

Step3: Solve for x

Cross - multiply: $71.5x=22\times97.5$. Then $x=\frac{22\times97.5}{71.5}$. Calculate $22\times97.5 = 2145$ and $\frac{2145}{71.5}=30$.

Answer:

30