Christine 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 55m, and the base of the smaller triangle has a length of 31m. The height of the smaller triangle is 20.2m. How wide is the river? Round your answer to the nearest meter.
Question
Christine 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 55m, and the base of the smaller triangle has a length of 31m. The height of the smaller triangle is 20.2m. How wide is the river? Round your answer to the nearest meter.
Solution
The problem involves similar triangles, which means the ratios of the corresponding sides are equal.
The ratio of the base of the smaller triangle to the base of the larger triangle is 31/55.
Since the triangles are similar, the ratio of the height of the smaller triangle to the width of the river (which is the height of the larger triangle) is also 31/55.
So, we can set up the equation:
20.2 / width of river = 31 / 55
To solve for the width of the river, we cross multiply and divide:
width of river = 20.2 * 55 / 31
After calculating the above expression, we get the width of the river to be approximately 36 meters when rounded to the nearest meter.
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