Question

the length of a rectangle is 8 feet more than its width the area of the rectangle is 84 square feet find its length and width.

Answer 1

x(x+8)=84
x²+8x=84
-84. -84
x²+8x-84=0
(x+14)(x-6)=0
x+14=0 x-6=0
x=-14 x=6
^reject the -14 because you can't have a negative measurement

The width is 6 feet and the length is 14 feet (6+8=14)

Answer 2

breath = 6ft

length = 14ft

Explanation:

Area of a rectangle = length x breath

Area = 84ft²

Since length is 8feet more than breath.

Let assume a breath is y.

i.e

breath = y

length = y + 8

Area = 84

84 = y * (y+8)

84 = y² + 8y

y² + 8y - 84 = 0

quadratic equation

y ( y - 6 ) + 14 ( y - 6 )

(y + 14 )( y - 6 )

So to find y

y + 14 = 0

y = -14

Or

y - 6 = 0

y = 6

We will you the positive value of y, because we can not have a negative value for measurements ( length or breath)

Therefore

breath = y

breath = 6ft

length = y + 8

length = 6 + 8 = 14ft