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) About Me  (Show Source):
You can put this solution on YOUR website!
The pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2. If you substitute in 5 and 12 for a and b respectively you get 5%5E2%2B12%5E2=25%2B144=169. sqrt%28169%29=13. 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:
5x%2B12x%2B13x=90. We can further simplify this equation so it becomes 30x=90. Now we must divide both sides of the equation by 30, so we get x=3. 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 13%2A3=39. Thus, the side lengths must be 15, 36, and 39 as 15%2B36%2B39=90. The longest side of the three is 39, so 39 is the answer.