Asked by Annika
A gardenervhas 100 meters of fencing to enclose two adjacent rectangular gardens. The gardener wants the enclosed area to be 400 sq meters. What dimensions should the gardener use to obtain this area?
Answers
Answered by
Steve
If the dimensions of the whole garden are x and 2y (because there are two adjacent gardens, each x by y),
2x+4y = 100
2xy = 400
or,
x+2y = 50
xy = 200
since x = 50-2y,
(50-2y)y = 200
50y - 2y^2 = 200
y^2-25y+100 = 0
y = 5 or 20
So, x = 40 or 10
The garden is 10 by 40.
2x+4y = 100
2xy = 400
or,
x+2y = 50
xy = 200
since x = 50-2y,
(50-2y)y = 200
50y - 2y^2 = 200
y^2-25y+100 = 0
y = 5 or 20
So, x = 40 or 10
The garden is 10 by 40.
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