Question

a rectangle has a width of 3x + 2 and a length of 2x - 1. what is the perimeter of the rectangle?
5x+1
8x - 6
10x+2
12x+4
question 6
2 pts
a rectangle has a width of 3x + 2 and a length of 2x - 1. what is the area of the rectangle?
6x^2 + 5x - 2
6x^2 + x - 2
4x^2 + 2x - 6
4x^2 + 4x - 6

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Given $w=3x + 2$ and $l = 2x-1$.

Step2: Substitute values into formula

$P=2((2x - 1)+(3x + 2))$.
First simplify the expression inside the parentheses: $(2x-1)+(3x + 2)=2x-1+3x + 2=5x + 1$.
Then $P = 2(5x + 1)=10x+2$.

Step3: Recall area formula

The area $A$ of a rectangle is $A=l\times w$. Substitute $w = 3x + 2$ and $l=2x - 1$.

Step4: Expand the product

$A=(2x - 1)(3x + 2)$.
Using the FOIL method:
First terms: $2x\times3x=6x^{2}$.
Outer terms: $2x\times2 = 4x$.
Inner terms: $-1\times3x=-3x$.
Last terms: $-1\times2=-2$.
Combining like - terms: $A=6x^{2}+4x-3x - 2=6x^{2}+x - 2$.

Answer:

Question 5: C. $10x + 2$
Question 6: B. $6x^{2}+x - 2$