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.)
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).
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