SOLUTION: the length of a room is two and half times its width. if the perimeter of the floor of the room is 70 m. find the length & width of the room.

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Question 100028: the length of a room is two and half times its width. if the perimeter of the floor of the room is 70 m. find the length & width of the room.
Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter is equal to the sum of all sides.
Since there are two sides that represent the length
and two sides that represent the width we can say the
perimeter = 2 times the length plus 2 times the width
OR
P = 2L + 2W
The problem tells us that the perimeter is 70 meters
so we can plug that in for P
70 = 2L + 2W
The problem also tells us that the length is two and half times the width
so L=2%261%2F2%28W%29
now we can plug that into the perimeter equation like this
70=2%282%261%2F2%28W%29%29%2B2W
Now we have and equation with only one variable W (width)
so lets solve for w
70=2%282%261%2F2%28W%29%29%2B2W
70=2%28%285W%29%2F2%29%2B2W
70=10W%2F2%2B2W
70=10W%2F2%2B4W%2F2
70=14W%2F2
140=14W
10=W
so we have found the width to be 10 meters
As stated above L=2%261%2F2%28W%29
so we can replace the W with 10 and solve for the length
L=2%261%2F2%28W%29
L=2%261%2F2%2810%29
L=%285%2F2%29%2810%29
L=50%2F2
L=25
Now we have found the length to be 25 meters
Check by using
70=2L%2B2W
70=2%2825%29%2B2%2810%29
70=50%2B20
70=70