A large rectangular movie screen in an IMAX theater has an area of 7,426 square feet. Find the dimensions of the screen if it is 15 feet longer than it is wide.

Answer 1

Let L = length of screen.

Let W = width of screen.

The screen is 15 feet longer than it is wide:

L = W+ 15

Area = L * W = (W+15) * W = W² + 15W = 7,426 square feet, or

W2 + 15W - 7426 = 0

Factoring: 7426 = 2* 47 * 79.

2 * 47 = 94

94 - 79 = 15.

So ( W - 79 ) * ( W + 94 ) and thus either

W = 79

or

W = -94.

Distance measurements can't be negative, so

W = 79 feet and L = W + 15 = 94 feet.

Answer 2