SOLUTION: A square room has a square rug in it. The area of the room not covered by the rug is 51 sq feet. The sum of the lenght of a side of the rug and the lenght of a side of the room i

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Question 79323: A square room has a square rug in it. The area of the room not covered by the rug is 51 sq feet. The sum of the lenght of a side of the rug and the lenght of a side of the room is 17 feet. Find the dimensions of the room.
I know Area=LenghtxWidth and Perimeter is 2Lenght + 2 Width, but I can't figure out this one. Please help.
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A square room has a square rug in it. The area of the room not covered by the rug is 51 sq feet. The sum of the lenght of a side of the rug and the lenght of a side of the room is 17 feet. Find the dimensions of the room.
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Draw the picture of the square room with the square rug in it.
Hint: put the square in the corner of the square room.
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Let a side of the square rug be x ft.
Let a side of the square room be y ft.
EQUATION:
x+y=17 ft
y=17-x
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The area of the square room is y^2=(17-x)^2
The area of the square rug is x^2
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EQUATION:
Area of room - Area of rug = 51 sq ft.
(17-x)^2-x^2=51
17^2-34x+x^2-x^2=51
17^2-51=34x
x=238/34
x=7 ft (the rug is 7'x7'
17-x=17-7=10 (the room is 10'x10')
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Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A square room has a square rug in it. The area of the room not covered by the rug is 51 sq feet. The sum of the length of a side of the rug and the length of a side of the room is 17 feet. Find the dimensions of the room.
:
Let x = 1 side of the room
Then x^2 = area of the room
:
Let (17-x) = 1 side of the square rug
Then (17-x)^2 = area of the rug
:
Room area - rug area = 51 sq/ft
x^2 - (17-x)^2 = 51
:
x^2 - (289 - 34x + x^2) = 51; FOILed (17-x)(17-x)
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x^2 - 289 + 34x - x^2 = 51; Removed the brackets, changed the signs
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34x = 51 + 289; x^2's eliminated, added 289 to both sides
:
34x = 340
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x = 340/34
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x = 10 ft is the side of the room
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17 - 10 = 7 ft is the side of the rug
:
:
Check, room area - rug area
10^2 - 7^2 = 51