Question

A room has an area of 60 square meters and a perimeter of 32 meters. What are the length and width of the room?

Answer 1

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Define x and y :
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Let the width be x.
Let the length be y. 

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Construct Equation:
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2x + 2y = 32 ---------- (1)
xy = 60         ---------- (2) 

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From Equation (1):
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2x + 2y = 32
x + y = 16
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sub x = 16 - y into (2)
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(16 -y)y = 60
16y - y² = 60
y² - 16² + 60 = 0
(y - 10)( y -6) = 0
y = 10 or y = 6

If y = 10, x = 6
If y = 6, x = 10

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Answer: Then length is 10m and the width is 6m.
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