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Jackson paints murals on walls. In order to paint one of his murals, he needs a rectangular area that is at least 4 feet wide and 3 feet high. The width and height have to increase by the same amount of feet, x . Which equation represents all the possible areas for the rectangular murals?

Respuesta :

MrRoyal

Answer:

[tex]Area = 12 + 7x + x^2[/tex]

Step-by-step explanation:

Given

Shape: Rectangle

Dimension: 4ft by 3ft

Increment: xft

Required

Determine the possible area of the rectangular mural

First, we need to determine the new dimension.

Since there's an increment of x, the new dimension is:

Dimension: 4 + x by 3 + x

Area is then calculated as:

[tex]Area = (4 + x)(3 + x)[/tex]

Open Brackets

[tex]Area = 12 + 4x + 3x + x^2[/tex]

[tex]Area = 12 + 7x + x^2[/tex]

The possible areas for the rectangular murals are [tex]A=(x+4)(x+3)[/tex] and [tex]A=x^2+7x+12[/tex].

Important information:

  • Width = 4 feet
  • Height = 3 feet
  • The width and height have to increase by the same amount of feet, x.

Area of rectangle:

After increasing the width and height, then new dimensions are:

Width = [tex]x+4[/tex] feet
Height = [tex]x+3[/tex] feet

The area of the rectangular murals is:

[tex]Area=Width\times height[/tex]

[tex]A=(x+4)(x+3)[/tex]

[tex]A=x^2+4x+3x+12[/tex]

[tex]A=x^2+7x+12[/tex]

Therefore, the possible areas for the rectangular murals are [tex]A=(x+4)(x+3)[/tex] and [tex]A=x^2+7x+12[/tex].

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