The hypotenuse will be 5 5​ feet long. The length of one leg of the triangle is 2 2​​ feet​ less​ than twice the other leg.

Question

The hypotenuse will be 55​ feet long. The length of one leg of the triangle is 22​​ feet​ less​ than twice the other leg. 



Answer 1

Since the hypotenuse of the (presumably) right triangle is given as 55, the sum of the squares of the two legs must be 55^2 = 3025. Denoting the legs by a and b, we have a^2 + b^2 = 3025, and a = 2b - 22 from the second clause in the problem. Substituting 2b - 22 for a, we get 4b^2 - 88b + 484 + b^2 = 3025, or 5b^2 - 88b - 2541 = 0. Hence, by the quadratic formula, b = (88 ± √(7744 + 50820))/10 = (88 ± √58564)/10 = (44 ± √14641)/5. Amazingly enough, 14641 is a perfect square, and its square root is 121. So we get b = 165/5 or -77/5, and, since a leg in a triangle cannot be negative, b = 33. Therefore, a = 2b - 22 = 44, and this triangle is just a multiple of the old 3-4-5 right triangle.