Question

a rectangle has an area of (x² - 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 expression

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

Step2: Relate to rectangle dimensions

Since \(A = lw\) and \(A=x^{2}-17x + 72=(x - 8)(x - 9)\), the length \(l=(x - 8)\) units and width \(w=(x - 9)\) units.

Answer:

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