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

Answer:

$W=(x-9)\ m$

Step-by-step 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

$A=(x^{2} -x-72)\ m^2$

$L=(x+8)\ m$

$W=\frac{A}{L}$

substitute

$W=\frac{(x^{2} -x-72)}{(x+8)}$

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

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

$x=\frac{1\pm\sqrt{289}} {2}$

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

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

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

so

$x^{2} -x-72=(x+8)(x-9)$  

substitute in the expression of W

$W=\frac{(x^{2} -x-72)}{(x+8)}$

$W=\frac{(x+8)(x-9)}{(x+8)}$

simplify

$W=(x-9)\ m$