Question

maria wants to measure the width of a river. she marks off two right triangles, as shown in the figure. the base of the larger triangle has a length of 59 m, the base of the smaller triangle has a length of 27 m. the height of the smaller triangle is 18.2 m. how wide is the river? round your answer to the nearest meter. (the figure is not drawn to scale.)

Explanation:

Step1: Set up proportion

Since the two right - triangles are similar, the ratios of their corresponding sides are equal. Let the width of the river be $x$ meters. The proportion is $\frac{18.2}{27}=\frac{x}{59}$.

Step2: Cross - multiply

Cross - multiplying gives us $27x = 18.2\times59$.

Step3: Calculate right - hand side

First, calculate $18.2\times59=18.2\times(60 - 1)=18.2\times60-18.2\times1 = 1092-18.2 = 1073.8$. So, $27x = 1073.8$.

Step4: Solve for $x$

$x=\frac{1073.8}{27}\approx39.77$.

Step5: Round to the nearest meter

Rounding $39.77$ to the nearest meter gives $x\approx40$.

Answer:

$40$