the rectangle below has an area of $x^{2}-x - 72$ square meters and a length of $x + 8$ meters. what…

the rectangle below has an area of $x^{2}-x - 72$ square meters and a length of $x + 8$ meters. what expression represents the width of the rectangle? width = meters

the rectangle below has an area of $x^{2}-x - 72$ square meters and a length of $x + 8$ meters. what expression represents the width of the rectangle? width = meters

Answer

Answer:

$x - 9$

Explanation:

Step1: Recall area formula

The area of a rectangle $A = l\times w$, where $A$ is area, $l$ is length and $w$ is width. We know $A=x^{2}-x - 72$ and $l=x + 8$, so $w=\frac{A}{l}=\frac{x^{2}-x - 72}{x + 8}$.

Step2: Factor the numerator

Factor $x^{2}-x - 72$. We need two numbers that multiply to -72 and add up to -1. The numbers are -9 and 8. So $x^{2}-x - 72=(x - 9)(x+8)$.

Step3: Simplify the fraction

Substitute the factored form into the width formula: $\frac{(x - 9)(x + 8)}{x + 8}$. Cancel out the common factor $(x + 8)$ (assuming $x\neq - 8$), and we get $w=x - 9$.