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

Question

3 years ago

9

. 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

1 answer:

pentagon [3] · Answer 1 · 2022-03-22T04:58:58+03:00

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

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