SOLUTION: If the floor of a room is a rectangle and it has a perimeter of 22 meters and area of 24 square meters what would be the length and width of this room? How do I calculate?

Question 749122: If the floor of a room is a rectangle and it has a perimeter of 22 meters and area of 24 square meters what would be the length and width of this room? How do I calculate?

Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Perimeter = 2 * length + 2 * width
Area = length * width
If we make length = x and width = y
then Perimeter = 2x + 2y
Area = xy
Make two equations:
2x + 2y = 22...1
xy = 24...2
Rearrange xy = 24 => x = 24/y
Substitute x = 24/y into (1)
2(24/y) + 2y = 22
48/y + 2y = 22
Take to one denominator - y
48 + 2y^2 = 22y
Sort out 2y^2 - 22y + 48 = 0
divide by 2
y^2 - 11y + 24 = 0
(y - 3)(y - 8) =0
So y = 3 or y = 8
Substituting in 2x + 2y = 22
2x + 2(3) = 22
2x = 22 - 6
2x = 16
x = 8
2x + 2y = 22
2x + 16 = 22
2x = 22 - 16
2x = 6
x = 3
So either length is 8m and width is 3m
or length is 3m and width is 8m

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