Hong wants to measure the width of a river. He marks off two right triangles, as shown in the figure. The base of the larger triangle has a length of 63m, and the base of the smaller triangle has a length of 35m. The height of the smaller triangle is 20.2m. How wide is the river? Round your answer to the nearest meter.
Question
Hong wants to measure the width of a river. He marks off two right triangles, as shown in the figure. The base of the larger triangle has a length of 63m, and the base of the smaller triangle has a length of 35m. The height of the smaller triangle is 20.2m. How wide is the river? Round your answer to the nearest meter.
Solution
The problem doesn't provide a figure, but based on the description, it seems like we're dealing with similar triangles. In similar triangles, the ratio of corresponding sides is equal.
Let's denote the width of the river as x.
The ratio of the base of the larger triangle to the base of the smaller triangle is 63m/35m = 1.8.
Since the triangles are similar, the ratio of their heights should be the same. So, the height of the larger triangle (which is the width of the river) to the height of the smaller triangle should also be 1.8.
Therefore, we can set up the following equation:
x/20.2m = 1.8
Solving for x gives us:
x = 1.8 * 20.2m = 36.36m
Rounding to the nearest meter, the width of the river is approximately 36 meters.
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