HELP Find A Simplified Expression For The Perimeter Of The Rug! CONFUESED? I Will Really Appreciate Your HELP?

HELP Find A Simplified Expression For The Perimeter Of The Rug! CONFUESED? I Will Really Appreciate Your HELP?
An area rug is to be purchased for a room that measures 10m by 8m. The area rug is to be centered on the wooden floor of the room so that the distance from the width of the rug to the nearest wall is twice the distance from the length of the rug to the nearest wall.

a) Find a simplified expression for the perimeter of the rug


b) Find the perimeter of the rug if x=2.5m

Diagram:
Picture a rectangle with another centered rectangle which is the rug. Use x to represent the distance.

Please explain how you answered both questions step by step. I will really appreciate your help.


Answers:

oscar_the_penguin:  below
2008-03-05 18:38:17
ohhyouhoeexo:  im confused to haha sooo sryy
2008-03-05 18:38:53
Chosen Answer
ck.choy:  Solution:

Let the distance of the wall to the width of the rug be x.

Therefore the width of the rug is (8 -x -x) = 8 -2x
legth of the rug = (10-2x -2x) =10-4x

Thus perimeter of the rug P = 2{(8-2x)+(10-4x)}
P = 2(18 - 6x) m

if x =2.5, P = 2( 18 -6*2.5) = 2 * 3 = 6m
2008-03-05 18:44:06
monica f:  Let x represent the distance b/w the wall and the rug.
Let L represent the length and W the width.
Let P represent the perimeter.

L=10-2x and W=8-2x

P= 2L + 2W
= 2(10-2x) + 2(8-2x)
= 20 - 4x + 16 - 4x
= 36 - 8x

Therefore P= 36 - 8x

For b) just sub x=2.5 into the equation P= 36 - 8x

so, P= 36 - 8(2.5)

This should be right =S but compare it to the other answerers I guess.
2008-03-05 18:50:48