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?
A.) x = –16

B.) x = –12

C.) x = 12

D.) x = 16

*The answer is D, x=16. If anyone wants to answer with an explanation of how this is the answer, I will reward them with brainliest.*

Answer 1

Answer:  D.) x = 16

Step-by-step explanation:

Given: The dimensions of the computer screen are modeled by the equation :

$x^2+(x-4)^2=20^2$

To find the value of x , we need to solve the equation.

Now, the above equation can be written as :

$x^2+x^2+16-8x=400\\\\\Rightarrow\ 2x^2-8x+16=400\\\\\Rightarrow2x^2-8x+384=0\\\\\Rightarrow\ 2(x^2-4x+192)=0\\\\\Rightarrow\ x^2-4x+192=0\\\\\Rightarrow(x-16)(x+12)=0\\\\\Rightarrow\ x=16\ or\ x=-12$

Since side cannot be negative therefore, x= 16

Answer 2

  x^2 +(x-4)^2 =20^2

  x^2 +(x-4)^2 =400

x^2 +(x-4)^2 -400=0

factor:

2x^2-8x-384=0

Factor the 2 out of 2X^2

2(x-16) (x+12) =0

 Divide both sides by 2

(x-16) (x+12) =0

X=16 , x=-12

 Number cannot be negative so x=16