Matt has a rectangular garden. The length of the garden is 8m shorter than 7 times its width. Find the length and width of the garden so that its area is atleast 12m.
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Area of the garden, A = 12m^2
Let the length of the garden be x metres.
Let the width of the garden be y metres.
Then, x = 7y - 8
A = length × breadth = xy
12 = ( 7y - 8) y
= 7y^2 - 8y
0 = 7y^2 - 8y - 12
= 7y^2 - 14y + 6y -12
= 7y (y - 2) + 6 (y - 2)
= (y - 2) (7y + 6)
y = 2 or -6/7(not possible)
The value of y is 2.
Therefore,
Breadth of the garden = y = 2 m
Length of the garden = 7y - 8
= 7(2) - 8
= 14 - 8 = 6 m
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