Respuesta :
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
[tex]Area=length\times width[/tex]
[tex]A_1=(x+5)\times x[/tex]
[tex]A_1=x^2+5x\text{ in}^2[/tex]
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
[tex]A_2=2(x+5)(x-1)[/tex]
[tex]A_2=(2x+10)(x-1)[/tex]
[tex]A_2=2x^2+10x-2x-10[/tex]
[tex]A_2=2x^2+8x-10 \text{ in}^2[/tex]
Area increased by 170 in².
[tex]A_2-A_1=170[/tex]
[tex](2x^2+8x-10)-(x^2+5x)=170[/tex]
[tex]2x^2+8x-10-x^2-5x=170[/tex]
[tex]x^2+3x-10=170[/tex]
Subtract 170 from both sides.
[tex]x^2+3x-10-170=0[/tex]
[tex]x^2+3x-180=0[/tex]
Splitting the middle term, we get
[tex]x^2+15x-12x-180=0[/tex]
[tex]x(x+15)-12(x+15)=0[/tex]
[tex](x+15)(x-12)=0[/tex]
[tex]x=-15,12[/tex]
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.
