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| Math Central | Quandaries & Queries |
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Question from Peter, a student: A rectangular room has a perimeter of 42 feet and an area of 108 square feet. What is the length, in feet, of the shorter side? |
Peter,
This room has a small, rectangular closet with a perimeter of 18 feet and an area of 14 square feet. The perimeter is distance around the 4 sided so if the lengths of the sides are x feet and y feet then 2x + 2y = 18 so
x + y = 9 feet.
The area is 14 square feet so
xy = 14 square feet.
From the first equation
y = 9 - x
and if you substitute this into the second equation you get
x (9 - x) = 14
9x - x2 = 14
x2 - 9x + 14 = 0
This equation factors
(x - 7)(x - 2) = 0
Thus x = 7 or x = 2 feet and hence the closet is 7 feet by 2 feet. What are he dimensions of the room?
Penny
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