Question

1. what is the formula for the perimeter of a rectangle?
2. what is the formula for the area of a rectangle?
3. write polynomials to represent the perimeter and the area of the rectangle.

perimeter:
area:

1. the length of a classroom is represented by the expression (10x + 6). the width of the classroom is represented by the expression (9x + 8).

draw a figure to represent the classroom.
write a polynomial that represents the perimeter of the classroom.
write a polynomial that represents the area of the classroom.

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width.

Step2: Recall area formula

The area formula of a rectangle is $A=l\times w$.

Step3: Find perimeter of rectangle in part 3

Given length $l = 2x - 1$ and width $w=x + 3$. Substitute into perimeter formula:
$P=2((2x - 1)+(x + 3))=2(2x-1+x + 3)=2(3x + 2)=6x+4$.

Step4: Find area of rectangle in part 3

Substitute length $l = 2x - 1$ and width $w=x + 3$ into area formula:
$A=(2x - 1)(x + 3)=2x\times x+2x\times3-1\times x - 1\times3=2x^{2}+6x - x-3=2x^{2}+5x - 3$.

Step5: Find perimeter of classroom

Given length $l = 10x + 6$ and width $w = 9x+8$. Substitute into perimeter formula:
$P=2((10x + 6)+(9x + 8))=2(10x+6 + 9x+8)=2(19x + 14)=38x+28$.

Step6: Find area of classroom

Substitute length $l = 10x + 6$ and width $w = 9x+8$ into area formula:
$A=(10x + 6)(9x + 8)=10x\times9x+10x\times8+6\times9x+6\times8=90x^{2}+80x+54x + 48=90x^{2}+134x + 48$.

Answer:

1. $P = 2(l + w)$
2. $A=l\times w$
3. Perimeter: $6x + 4$, Area: $2x^{2}+5x - 3$
4. Perimeter: $38x+28$, Area: $90x^{2}+134x + 48$