Question

The dimensions of a rectangular monitor screen are such that it's length is 5 in. More than it's width. If the length were doubled and if the width were deceased by 1 in the area would be increased by 170 in^2. What are the length and width of the screen?

Answer 1

Given:

Length of a rectangular monitor screen is 5 in more than it's width.

If the length were doubled and if the width were deceased by 1 in the area would be increased by 170 in².

To find:

The length and width of the screen.

Solution:

Let width of the screen be x inches.

Length of a rectangular monitor screen is 5 in more than it's width. So,

Length of screen = (x+5) inches

Area of screen is

`Area=length* width`

`A_1=(x+5)* x`

`A_1=x^2+5x\text{ in}^2`

If the length were doubled and if the width were deceased by 1 in the area would be increased by 170 in².

New length = 2(x+5) inches

New width = (x-1) inches

So, new area is

`A_2=2(x+5)(x-1)`

`A_2=(2x+10)(x-1)`

`A_2=2x^2+10x-2x-10`

`A_2=2x^2+8x-10 \text{ in}^2`

Area increased by 170 in².

`A_2-A_1=170`

`(2x^2+8x-10)-(x^2+5x)=170`

`2x^2+8x-10-x^2-5x=170`

`x^2+3x-10=170`

Subtract 170 from both sides.

`x^2+3x-10-170=0`

`x^2+3x-180=0`

Splitting the middle term, we get

`x^2+15x-12x-180=0`

`x(x+15)-12(x+15)=0`

`(x+15)(x-12)=0`

`x=-15,12`

Width cannot be negative. So, x=12.

Width = 12 inches

Length = 12+5 = 17 inches

Therefore, the length of screen is 17 inches and width is 12 inches.