a rectangle has an area of (x² - 17x + 72) square units. since the area of a rectangle is determined using…

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?\nlength = (x - 8) units and width = (x - 9) units\nlength = (x + 9) units and width = (x + 8) units\nlength = (x - 6) units and width = (x - 12) units\nlength = (x + 12) units and width = (x + 6) units

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?\nlength = (x - 8) units and width = (x - 9) units\nlength = (x + 9) units and width = (x + 8) units\nlength = (x - 6) units and width = (x - 12) units\nlength = (x + 12) units and width = (x + 6) units

Answer

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: Compare with length - width formula

Since the area of a rectangle (A = lw) and (A=x^{2}-17x + 72=(x - 8)(x - 9)), the length and width could be ((x - 8)) units and ((x - 9)) units respectively.

Answer:

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