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Two triangles are similar. One has sides of 8 m, 5 m, and 6 m. If the longest side of the second triangle is 7 m, what are the length of the shortest side of the second triangle? (Answer to two decimal places.)

Question

Two triangles are similar. One has sides of 8 m, 5 m, and 6 m. If the longest side of the second triangle is 7 m, what are the length of the shortest side of the second triangle? (Answer to two decimal places.)

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Solution

The two triangles are similar, which means their sides are proportional.

First, we need to identify the longest side of the first triangle. That would be 8 m.

Next, we set up a proportion to find the length of the shortest side of the second triangle. The proportion is (longest side of first triangle)/(shortest side of first triangle) = (longest side of second triangle)/(shortest side of second triangle).

Substituting the given values into the proportion gives us 8/5 = 7/x.

To solve for x, we cross-multiply to get 8x = 35.

Finally, we divide both sides by 8 to solve for x, which gives us x = 35/8 = 4.375 m.

So, the length of the shortest side of the second triangle is 4.38 m (rounded to two decimal places).

This problem has been solved

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