The length of the photograph is 10 inches.
Explanation:
Given, Width of a photograph is x.
Length of the photograph is 3 inches longer than its width. i.e. x + 3.
Area of the photograph = x(x+3)
If its area is 70 square inches, then
x(x+3)=70
[tex]x^2 + 3x = 70[/tex]
[tex]x^2 + 3x-70 = 0[/tex]
[tex]x^2 - 7x + 10x-70 = 0[/tex]
x(x-7)+10(x-7)=0
(x+10)(x-7) =0
x+10=0; x-7 = 0
x = -10 and x = 7
Width of the photograph must not be in negative value. So, we can ignore –10.
Therefore, width of the photograph, x = 7 inches.
Now, the length of the photograph = 7 + 3 = 10 inches.
Thus, the required length of the photograph is 10 inches.
