# SOLUTION: the perimeter of a right triangle is 90 ft. the ratio of the legs is 5:12. what is the length of the longest leg of the triangle?

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 Question 621037: the perimeter of a right triangle is 90 ft. the ratio of the legs is 5:12. what is the length of the longest leg of the triangle?Answer by matt501823(7)   (Show Source): You can put this solution on YOUR website!The pythagorean Theorem is . If you substitute in 5 and 12 for a and b respectively you get . . Thus the ratios of the sides must be 5, 12, and 13. Now we know that in order to maintain this ratio we must multiply the sides by a common factor such that the perimeter equals 90. To do this we can create the following equation: . We can further simplify this equation so it becomes . Now we must divide both sides of the equation by 30, so we get . Now that we know that the common factor is 3 we can simply multiply the side length with a ratio of 13 by 3 and we get . Thus, the side lengths must be 15, 36, and 39 as . The longest side of the three is 39, so 39 is the answer.