Question

the rectangle below has an area of $x^{2}-25$ square meters and a length of $x + 5$ meters. what expression represents the width of the rectangle? width $x+5$ $x^{2}-25$ width = meters show calculator

Explanation:

Step1: Recall area formula

$A = l\times w$ (where $A$ is area, $l$ is length, $w$ is width). So $w=\frac{A}{l}$.

Step2: Substitute given values

We have $A=x^{2}-25$ and $l = x + 5$. Then $w=\frac{x^{2}-25}{x + 5}$.

Step3: Factor the numerator

$x^{2}-25=(x + 5)(x - 5)$ (using difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$, here $a=x$ and $b = 5$).

Step4: Simplify the fraction

$w=\frac{(x + 5)(x - 5)}{x + 5}=x - 5$ (assuming $x
eq - 5$).

Answer:

$x - 5$