Question

the area of a rectangle is given. identify the missing terms in the length and width. the length and width of the rectangle are represented by the expressions (x + ) and ( + 4). question 1 of 30 review progress video textbook get more help - clear all back next check answer x²+11x + 28 (x + ) ( + 4)

Explanation:

Step1: Recall area formula

The area of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Given $A=x^{2}+11x + 28$ and assume $w=x + 4$.

Step2: Factor the area expression

We factor $x^{2}+11x + 28$. We need to find two numbers that multiply to $28$ and add up to $11$. The numbers are $4$ and $7$. So $x^{2}+11x + 28=(x + 4)(x+7)$.

Step3: Find the length

Since $A=l\times w=(x + 4)(x + 7)$ and $w=x + 4$, then $l=x + 7$.

Answer:

The length is $(x + 7)$ and the width is $(x + 4)$.