Question

a rectangle has an area of $(x^2 - 17x + 72)$ square units. since the area of a rectangle is determined using the formula, $a = lw$, what could be the length and width of the rectangle?

• length = $(x - 8)$ units and width = $(x - 9)$ units
• length = $(x + 9)$ units and width = $(x + 8)$ units
• length = $(x - 6)$ units and width = $(x - 12)$ units
• length = $(x + 12)$ units and width = $(x + 6)$ units

Explanation:

Step1: Factor the quadratic

We need to factor \(x^2 - 17x + 72\). We look for two numbers that multiply to \(72\) and add to \(-17\). The numbers are \(-8\) and \(-9\) because \((-8)\times(-9)=72\) and \(-8 + (-9)=-17\).
So, \(x^2 - 17x + 72=(x - 8)(x - 9)\).

Step2: Match with length and width

Since the area of a rectangle is \(A = lw\), and the area is \((x - 8)(x - 9)\), the length and width could be \((x - 8)\) units and \((x - 9)\) units (or vice versa).

Answer:

A. length = (x - 8) units and width = (x - 9) units