Question

A computer company makes a rectangular screen with a diagonal of 20 inches. The width of the screen is 4 inches less than its length. The dimensions of the computer screen are modeled by the equation x2 + (x – 4)2 = 202. What is the value of x, the length of the screen? x = –16 x = –12 x = 12 x = 16

Answer 1

x = 16

Explanation:

The answer above is correct.

Answer 2

Explanation:

x = length of screen

x-4 = width of screen

x² + (x-4)² = 20²

x² + (x²-8x+16) = 400

2x² - 8x - 384 = 0

x² - 4x - 192 = 0

use the quadratic formula to solve for x

x = [4 ± √(4²-4·1(-192))]/[2·1]

= [4 ± √784]/2

= 4 ± 28]/2

= 16, -12

-12 is an extraneous solution, so x = 16 inches.

:::::

Exponents need to be marked with a ^. For example, (x-4)² can be written (x-4)^2.