Question

The dimensions of a rectangular monitor screen are such that it’s length is 4 in. more than it’s width. If the length were doubled and if the width were decreased by 1 in., the area would be increased by 216 in^2. What are the length and width of the screen?

Answer 1

Answer:

14 inches by 18 inches

Step-by-step explanation:

Old rectangular monitor screen:

Width = x in

Length = x + 4 in

Area $=x(x+4)\ in^2$

New rectangular monitor screen:

Width = x - 1 in

Length = 2(x + 4) in

Area $=(x-1)(2(x+4))=2(x-1)(x+4)\ in^2$

This area would be increased by $216\ in^2,$ so the area would be equal to $x(x+4)+216\ in^2$. Hence,

$2(x-1)(x+4)=x(x+4)+216\\ \\2(x^2+4x-x-4)=x^2+4x+216\\ \\2x^2+6x-8-x^2-4x-216=0\\ \\x^2+2x-224=0\\ \\D=2^2-4\cdot (-224)=4+896=900\\ \\x_{1,2}=\dfrac{-2\pm \sqrt{900}}{2}=\dfrac{-2\pm 30}{2}=-16,\ 14$

The width cannot be negative, so

Width = 14 in

Length = 14 + 4 = 18 in