Question

A photograph has a length that is 3

inches longer than its width, x. So its area is given by the expression x(x+3)
square inches. If the area of the photograph is 70
square inches, what is the length of the photograph?

The length of the photograph is blank inches.

Answer 1

length of the photograph = 10 inches

Explanation:

as per given:

width of the photograph = x inches

length of the photograph = x + 3 inches

area = length * width = x(x + 3)

area of the photograph = 70 inches²

i.e.

70 = x(x + 3)

70 = x² + 3x

x² + 3x - 70 = 0

x² - 7x + 10x - 70 = 0

x(x - 7) + 10(x - 7) = 0

(x + 10)(x - 7) = 0

thus,

x = -10 or x = 7

as in our assumption x is the width of the photograph so we will take the positive value for x

i.e.

width of the photograph = x = 7 inches

length of the photograph = x + 3 = 7 + 3 = 10 inches