Question

1. the area of a rectangle is found by multiplying the length by the width. in the rectangle below, the area of the rectangle is equal to the expression 2x² - 27x + 70. an expression equal to the length is shown on the diagram. which of the following expressions is equal to the width of the rectangle? a. x + 10 b. x - 10 c. 2x + 10 d. 2x - 10

Explanation:

Step1: Recall area formula

The area of a rectangle $A = l\times w$, where $l$ is length and $w$ is width. Given $A=2x^{2}-27x + 70$ and $l = 2x - 7$. We need to find $w=\frac{A}{l}$, so we divide $2x^{2}-27x + 70$ by $2x - 7$.

Step2: Factor the area expression

Factor $2x^{2}-27x + 70$. We need two numbers that multiply to $2\times70 = 140$ and add up to $-27$. The numbers are $-7$ and $-20$. So $2x^{2}-27x + 70=2x^{2}-7x-20x + 70=x(2x - 7)-10(2x - 7)=(2x - 7)(x - 10)$.

Step3: Calculate the width

Since $w=\frac{A}{l}$ and $A=(2x - 7)(x - 10)$ and $l = 2x - 7$, then $w=\frac{(2x - 7)(x - 10)}{2x - 7}=x - 10$.

Answer:

B. $x - 10$