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jmc

geometry intermediate

Problem

Two sides of an isosceles triangle are 10 inches and 20 inches. If the shortest side of a similar triangle is 50 inches, what is the perimeter of the larger triangle?
Solution
First of all, the third side of the smaller triangle cannot be 10 inches because sides of 10, 10 and 20 inches would not form a triangle. The smaller triangle must have sides of 10, 20 and 20 inches. If the shortest side of the similar triangle is 50 inches, then the other two sides are 100 inches and 100 inches. Thus, the perimeter of the larger triangle is .
Final answer
250\text{ inches}