Asked by hary

Rectangle garden using a wall as one side of the perimeter. What are the dimensions if we have 16ft of fencing and an area of 30sqft.
To be clear, you are only using the fencing for 3 sides of the garden.
Answered by roger
well, Two of the sides would have to be either 5 or 3. Because 5+5+6=16 and 5x6=30 or 3+3+10=16 and 3x10=30.
Does this help?
Answered by hary
No that does not help. Although that is probably the answer how does it get solved algebraically?
Answered by Steve
If the side of length x is parallel to the wall, then

x + 2y = 16
xy = 30
(16-2y)y = 30
2y^2 - 16y + 30 = 0
y^2-8y+15 = 0
(y-3)(y-5) = 0
y = 3 or 5
so, x = 10 or 6

The garden is 10x3 or 6x5
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