Question

sailing the two sailboats shown are participating in a regatta. if the sails are similar, what is the value of x? express your answer as a decimal if necessary. 168.5 in. 220 in. 40° 264 in. 40°

Explanation:

Step1: Set up the proportion

Since the sails are similar, the ratios of corresponding sides are equal. So, we have the proportion \(\frac{168.5}{220}=\frac{x}{264}\).

Step2: Solve for \(x\)

Cross - multiply: \(220x = 168.5\times264\).
First, calculate \(168.5\times264=(168 + 0.5)\times264=168\times264+0.5\times264\).
\(168\times264=(170 - 2)\times264 = 170\times264-2\times264=44880 - 528 = 44352\), and \(0.5\times264 = 132\). So \(168.5\times264=44352+132 = 44484\).
Then, \(x=\frac{44484}{220}=202.2\).

Answer:

\(202.2\)