Question

jane 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 56 m, and the base of the smaller triangle has a length of 27 m. the height of the smaller triangle is 21.1 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

Let $w$ = river width. Similar triangles give:
$\frac{w}{56} = \frac{21.1}{27}$

Step2: Solve for $w$

Multiply both sides by 56:
$w = 56 \times \frac{21.1}{27}$

Step3: Calculate value

Compute the product and division:
$w = \frac{56 \times 21.1}{27} = \frac{1181.6}{27} \approx 43.76$

Step4: Round to nearest meter

Round 43.76 to whole number:
$w \approx 44$

Answer:

44 m