a rectangle has an area of $(x^{2}-17x + 72)$ square units. since the area of a rectangle is determined…

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?\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 $(x^{2}-17x + 72)$ 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?\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). So, (x^{2}-17x + 72=(x - 8)(x - 9)) using the formula ((x+a)(x + b)=x^{2}+(a + b)x+ab).

Step2: Recall the area formula

Since the area of a rectangle (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