Problema Solution
the perimeter of a rectangle is 68cm.if the diagonal is 26cm.find the di.mensions of the rectangle
Answer provided by our tutors
Let L = length and W = width of the rectangle
We know the perimeter is 68, so L+W = 34, and:
L = 34 - W
Using the Pythagorean theorem, with the diagonal as the hypotenuse, we know:
L² + W² = 26²
Using substitution, we can solve for W:
(34 - W)² + W² = 26²
1156 - 68W + 2W² = 676
2W² - 68W + 480 = 0
W² - 34W + 240 = 0
(W - 10)(W - 24) = 0