Question

The rectangle below has an area of x to the second power minus x minus 72 square meters and a length of x plus 8 meters. What expression represents the width of the rectangle?

Answer 1

`W=(x-9)\ m`

Explanation:

we know that

The area of rectangle is equal to

`A=LW`

where

L is the length of rectangle

W is the width of rectangle

we have

`A=(x^(2) -x-72)\ m^2`

`L=(x+8)\ m`

`W=(A)/(L)`

substitute

`W=((x^(2) -x-72))/((x+8))`

Solve the quadratic equation in the numerator

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

`x=\frac{-b\pm\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`x^(2) -x-72=0`

so

`a=1\\b=-1\\c=-72`

substitute in the formula

`x=\frac{-(-1)\pm\sqrt{-1^(2)-4(1)(-72)}} {2(1)}`

`x=\frac{1\pm√(289)} {2}`

`x=\frac{1\pm17} {2}`

`x=\frac{1+17} {2}=9`

`x=\frac{1-17} {2}=-8`

so

`x^(2) -x-72=(x+8)(x-9)`

substitute in the expression of W

`W=((x^(2) -x-72))/((x+8))`

`W=((x+8)(x-9))/((x+8))`

simplify

`W=(x-9)\ m`