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Olenka [21]
3 years ago
9

A bedroom is in the shape of a rectangle. The length of the bedroom is represented by 3x^2 and the width is represented by 7x+14

. The square rug has a length of 4x +3 what is the area of the bedroom that is not covered by the rug?
PLEASE HELP
Mathematics
1 answer:
pentagon [3]3 years ago
6 0

The area of the room that is not covered by the rug is: 21x^3+26x^2-24x+9

Step-by-step explanation:

Let L be the length of the room

and

W be the width of the room

Then

L = 3x^2

W = 7x+14

Area of the bedroom:

A_r = L*W\\=3x^2(7x+14)\\=21x^3+42x^2

Area of Rug:

Let S be the side of rug

S = 4x+3

A_{rug} =S^2\\=(4x+3)^2\\=(4x)^2+2(4x)(3)+(3)^2\\=16x^2+24x+9

The area of the room that is not covered by the rug will be obtained by subtracting the area of the rug from the area of the room.

So,

Area\ of\ room\ not\ covered\ by\ rug =A_r - A_{rug}\\= 21x^3+42x^2-(16x^2+24x+9)\\=21x^3+42x^2-16x^2-24x-9\\=21x^3+26x^2-24x+9

Hence,

The area of the room that is not covered by the rug is: 21x^3+26x^2-24x+9

Keywords: Rectangle, square

Learn more about area at:

  • brainly.com/question/10703930
  • brainly.com/question/10772025

#LearnwithBrainly

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7 0
3 years ago
Need help on this question 36
frosja888 [35]
For the bottom, to find the top side of the triangle, 10-4, as seen from the top and bottom sides of the rectangle. So 6.

To find  the left side of triangle, subtract 12 from 8. 12 from the left and 8 from the rectangle. This gives you 4.

Now that we have 6 and 4, we can find the area:

A= ab/2

A= (6*4)/2

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