SOLUTION: A rectangular countertop has an area of 27 square feet. Its perimeter is 24 feet. What are the dimensions of the counter?
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-> SOLUTION: A rectangular countertop has an area of 27 square feet. Its perimeter is 24 feet. What are the dimensions of the counter?
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A rectangular countertop
has an area of 27 square feet.
Area = length x breadth
xy = 27.......(1)
x = 27/y.......(1)
Its perimeter is 24 feet.
Perimeter = 2 x width + 2 x length
24 = 2x + 2y
2x + 2y = 24.......(2)
Substitute x = 27/y into Eq(2)
2(27/y) + 2y = 24
54/y + 2y = 24
Multiply through by y
54 + 2y^2 = 24y
Sort into ax^2 + bx + c form
2y^2 - 24y + 54
Divide by 2
2(y^2 - 12y + 27)= 0
2(y - 3)(y - 9) = 0
y - 3 = 0
y = 3
y - 9 = 0
y = 9
By substituting either y = 3
back into Eq(1)
x = 27/y
x = 27/3
x = 9
or Substituting y = 9
back into Eq(1)
x = 27/y
x = 27/9
x = 3
So, either your breadth is 3ft
and the length is 9ft
or
breadth is 9ft
and the length is 3ft
Hope this helps :-)
