Question

The rectangle below has an area of 70 square meters.

Find the dimensions of the rectangle.
(x - 11)
(x - 8)

Answer 1

The side lengths are 10 by 7

Explanation:

The area of a rectangle is

A = l*w

70 = (x - 11)(x - 8)

FOIL

70 = x^2 -8x-11x+88

Combine like terms

70 = x^2 -19x +88

Subtract 70 from each side

0 = x^2 -19x +88-70

0 = x^2 -19x+18

Factor

What number multiplies to 18 and adds to -19

-18*-1 =18

-18-1 = -19

0=(x-18)(x-1)

Using the zero product property

x-18=0 x-1=0

x=18 x=1

But x cannot x=1 because then the side lengths would be negative

x-18 = 10

x-11 = 7

The side lengths are 10 by 7