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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.

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 a class=

Respuesta :

devishri1977

Answer:

2x² + 12x

Step-by-step 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

semsee45

Answer:

[tex]2x^2+12x[/tex]

Step-by-step 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.

[tex]\boxed{\textsf{Area of a rectangle}=\sf length \times width}[/tex]

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

[tex]\implies \textsf{Area of Poster 1}=x(x+5)[/tex]

[tex]\implies \textsf{Area of Poster 2}=x(x+7)[/tex]

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:

[tex]\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}[/tex]

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