Question

The rectangle below has an area of x^2−4x−12, squared, minus, 4, x, minus, 12 square meters and a length of x+2x+2 x+2 x, plus, 2 meters. What expression represents the width of the rectangle?

Answer 1

Answer:

$W=(x-6)\ m$

Step-by-step explanation:

we know that

The area of rectangle is given by the formula

$A=LW$

we have

$A=(x^2-4x-12)\ m^2$

$L=(x+2)\ m$

substitute

$x^2-4x-12=(x+2)W$

Solve the quadratic equation of the left side

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

$x^2-4x-12=0$  

so

$a=1\\b=-4\\c=-12$

substitute in the formula

$x=\frac{-(-4)\pm\sqrt{-4^{2}-4(1)(-12)}} {2(1)}$

$x=\frac{4\pm\sqrt{64}} {2}$

$x=\frac{4\pm8} {2}$

$x=\frac{4+8} {2}=6$

$x=\frac{4-8} {2}=-2$

therefore

$x^2-4x-12=(x+2)(x-6)$  

substitute in the formula of area

$(x+2)(x-6)=(x+2)W$

solve for W

simplify

$W=(x-6)\ m$