Question

the rectangle below has an area of $x^2 - 144$ square meters and a length of $x + 12$ meters. what expression represents the width of the rectangle? image of a rectangle with length $x + 12$, area $x^2 - 144$, and width to be found width = blank meters

Explanation:

Step1: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \). So, to find the width, we can rearrange this formula to \( \text{width} = \frac{A}{\text{length}} \).

Step2: Factor the area expression

The area is \( x^2 - 144 \), which is a difference of squares. The formula for a difference of squares is \( a^2 - b^2 = (a + b)(a - b) \). Here, \( a = x \) and \( b = 12 \), so \( x^2 - 144 = (x + 12)(x - 12) \).

Step3: Divide the factored area by the length

The length is \( x + 12 \). So, the width is \( \frac{(x + 12)(x - 12)}{x + 12} \). We can cancel out the \( x + 12 \) terms (assuming \( x
eq -12 \), which makes sense in the context of length being positive), leaving us with \( x - 12 \).

Answer:

\( x - 12 \)