Ok, so x * y = 144 and 2x + 2y = 68. That means y = 144/x and x + y = 34, you with me so far? Now, substituting for y..... x + (144/x) = 34. Now subtract x and you have 144/x = 34 - x Times both sides by x. 144 = x(34-x) So you have 34x - x^2 = 144. -x^2 + 34x - 144 = 0 Times through by a -1: x^2 - 34x + 144 = 0 Now factor. Using the quadratic formula, I get 35.06 and 8.94 Ok, so we know that the side we labeled x either equals 35.05 or 8.94. Now, we plug those back into the original equation (x + y = 34) 35.05 + y = 34... y = -1.05 8.94 + y = 34 .... y - 25.06 Knowing that a side can't be negative, we now know one side is 8.94 and the other is 24.06. Now we can use the Pythagorean theorem to get the diagonal. a^2 + b^2 = c^2 (8.94)^2 + (25.06)^2 = c^2 79.9 + 628 = c^2 707.9 = c^2 Take the square root of both sides... And the diagonal is: 26.61! Good luck, hoped that helped. I may have round off error, but it's close enough.