SOLUTION: Mary's living room is 12'x20'. She wants to buy a carpet that will leave an equal border on all sides. If the area of the border is to be 1/3 of the area of the carpet, how big a c

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Mary's living room is 12'x20'. She wants to buy a carpet that will leave an equal border on all sides. If the area of the border is to be 1/3 of the area of the carpet, how big a c      Log On

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Question 988568: Mary's living room is 12'x20'. She wants to buy a carpet that will leave an equal border on all sides. If the area of the border is to be 1/3 of the area of the carpet, how big a carpet should Mary buy?
Found 2 solutions by josgarithmetic, Timnewman:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let u be the size of the border's width at all four sides.
The carpet area would be %2812-2u%29%2820-2u%29;
The room area is 12%2A20;
The border area is 12%2A20-%2812-2u%29%2820-2u%29.

Border area must be one-third the area of the carpet:
highlight_green%2812%2A20-%2812-2u%29%2820-2u%29=%281%2F3%29%2812-2u%29%2820-2u%29%29
Let me skip a couple of steps...
3%2A64u-12u%5E2=240-64u%2B4u%5E2
4u%5E2-64u%2B240%2B12u%5E2-3%2A64u=0
16u%5E2-64u-3%2A64u%2B240=0
16u%5E2-64%2A4u%2B240=0
highlight_green%28u%5E2-16u%2B15=0%29
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Use formula for general solution of quadratic equation. Can you finish this?

Discriminant is... 14%5E2.
The form you want is u=%2816-14%29%2F2=2%2F2=1.

Answer by Timnewman(323) About Me  (Show Source):
You can put this solution on YOUR website!
Hi dear,
Since her room measure 12*20,
Area of her room=12*20
=240sqrt unit.
If area of the border is 1/3 area of the room.
Then,
Area of the border=240/3
=60squt sunit
Area of the carpet mary will buy =240-60
=180squrt unit
The mearsure of area of carpet to be buy is 180squrt unit.
HOPE THIS HELPS?
::TIMNEWMAN::