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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 64m, and the base of the smaller triangle has a length of 34m. The height of the smaller triangle is 17.8m. How wide is the river? Round your answer to the nearest meter.

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 64m, and the base of the smaller triangle has a length of 34m. The height of the smaller triangle is 17.8m. How wide is the river? Round your answer to the nearest meter.

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Solution

The problem doesn't provide a figure, but based on the information given, we can assume that the two right triangles are similar (since they are both right triangles and share an angle).

In similar triangles, the ratio of corresponding sides is equal. So, we can set up a proportion to find the width of the river (which is the height of the larger triangle).

Let's denote the width of the river (the height of the larger triangle) as x.

We know that the ratio of the base of the smaller triangle to the height of the smaller triangle (34/17.8) is equal to the ratio of the base of the larger triangle to the height of the larger triangle (64/x).

So, we can set up the following equation:

34/17.8 = 64/x

To solve for x, we can cross-multiply:

34x = 6417.8

Then, divide both sides by 34 to solve for x:

x = (64*17.8) / 34

After calculating the above expression, we find that x is approximately 33.6 meters.

Rounding to the nearest meter, the width of the river is approximately 34 meters.

This problem has been solved

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