Question

Augustina has 2 posters with length x inches.

One poster has a width of x + 5 inches, and
the other has a width of x + 7 inches. Write an
expression to represent the area of wall that the
posters will cover.

Answer 1

2x² + 12x

Explanation:

Area of rectangle:

Area of rectangle = length * width

Poster 1:

length = x inches

widht = (x + 5) inches

Area of poster 1 = x * (x + 5)

= x*x + x*5 {Distributive property}

= x² + 5x square inches

Poster 2:

length = x inches

width = (x + 7) inches

Area of poster =x *(x+ 7)

= x*x + x*7

= x² + 7x

Area of wall = area of poster1 + area of poster 2

= x²+ 5x + x² + 7x

= x² + x² + 5x + 7x {Combine like terms}

= 2x² + 12x

Answer 2

`2x^2+12x`

Explanation:

Dimensions of Poster 1:

• Length = x inches
• Width = (x + 5) inches

Dimensions of Poster 2:

• Length = x inches
• Width = (x + 7) inches

The posters can be modeled as rectangles.

`\boxed{\textsf{Area of a rectangle}=\sf length * width}`

Therefore, the expressions for the area of each poster are:

`\implies \textsf{Area of Poster 1}=x(x+5)`

`\implies \textsf{Area of Poster 2}=x(x+7)`

Therefore, the expression that represents the area of the wall that the posters will cover is the sum of the expressions of the areas of the individual posters:

`\begin{aligned}\textsf{Area of wall posters will cover}&=\textsf{Area of Poster 1}+\textsf{Area of Poster 2}\\& = x(x+5)+x(x+7)\\&=x^2+5x+x^2+7x\\&=x^2+x^2+5x+7x\\&=2x^2+12x\end{aligned}`