Question

A large rectangular movie screen in an IMAX theater has an area of 8,364 square feet. Find the dimensions of the screen if it is 20 feet longer than it is wide.

Answer 1

The dimensions of the screen are

Length:102 feet

Width: 82 feet

Explanation:

we know that

The area of the rectangle (movie screen) is equal to

`A=LW`

where

L is the length

W is the width

we have

`A=8,364\ ft^2`

so

`8,364=LW` ----> equation A

The screen is 20 feet longer than it is wide.

so

`L=W+20` ---> equation B

substitute equation B in equation A

`8,364=(W+20)W`

solve for W

`8,364=W^2+20W\\W^2+20W-8,364=0`

solve the quadratic equation by graphing

the solution is W=82 ft

see the attached figure

Find the value of L

`L=82+20=102\ ft`

therefore

The dimensions of the screen are

Length:102 feet

Width: 82 feet