Answer:
Length = 20.49 yards and Width = 12.49 yards.
Step-by-step explanation:
The area of the rectangular playground is given by 256 yards square. It is also known that one of the sides of the playground is 8 yards longer than the other side. Therefore, let the smaller side by x yards. Then the longer side will be (x+8) yards. The area of the rectangle is given by:
Area of the rectangle = length * width.
256 = x*(x+8)
x^2 + 8x = 256. Applying the completing the square method gives:
(x)^2 + 2(x)(4) + (4)^2 = 256 + 16
(x+4)^2 = 272. Taking square root on both sides gives:
x+4 = 16.49 or x+4 = -16.49 (to the nearest 2 decimal places).
x = 12.49 or x = -20.49.
Since length cannot be negative, therefore x = 12.49 yards.
Since smaller side = x yards, thus smaller side = 12.49 yards.
Since larger side = (x+8) yards, thus larger side = 12.49+8 = 20.49 yards.
Thus, the length and the width to minimize the perimeter of fencing is 20.49 yards and 12.49 yards respectively!!!
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