Question

lashonda 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, and the base of the smaller triangle has a length of 27 m. the height of the smaller triangle is 16.4 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 ratio of the bases of the two triangles is equal to the ratio of their heights. So we have the proportion $\frac{27}{59}=\frac{16.4}{x + 16.4}$.

Step2: Cross - multiply

Cross - multiplying gives us $27(x + 16.4)=59\times16.4$.
Expanding the left - hand side: $27x+27\times16.4 = 59\times16.4$.
$27x+442.8=967.6$.

Step3: Solve for $x$

Subtract 442.8 from both sides: $27x=967.6 - 442.8$.
$27x = 524.8$.
Then divide both sides by 27: $x=\frac{524.8}{27}\approx19.4$.

Answer:

$19.4$