Question

6. The perimeter of a rectangle is 68 cm. If the diagonal is 26 cm find
the dimensions of the rectangle.​

Answer 1

Answer:

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

The dimensions of the rectangle are 10 cm x 24 cm.

Hey! Mate Here is your solution. Thanks