Question

the rectangle below has an area of 81 - x^2 square meters and a width of 9 - x meters. what expression represents the length of the rectangle? length = meters

Explanation:

Step1: Recall area formula

$A = lw$ (where $A$ is area, $l$ is length, $w$ is width). We know $A=81 - x^{2}$ and $w = 9 - x$, so $l=\frac{A}{w}=\frac{81 - x^{2}}{9 - x}$.

Step2: Factor the numerator

$81 - x^{2}$ is a difference - of - squares. Using the formula $a^{2}-b^{2}=(a + b)(a - b)$, where $a = 9$ and $b=x$, we have $81 - x^{2}=(9 + x)(9 - x)$.

Step3: Simplify the fraction

$l=\frac{(9 + x)(9 - x)}{9 - x}$. Since $x
eq9$ (otherwise the width is 0), we can cancel out the $(9 - x)$ terms, and we get $l = 9 + x$.

Answer:

$9 + x$