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The dmension of the rectangle with perimeter of 68 m has the largest possible area as 17m by 17m.
perimeter of rectangle = 2(l + w)
where
Therefore,
perimeter = 68 m
68 = 2l + 2w
l + w = 34
l = 34 - w
Hence, the largest possible area is at the amximum.
area = lw
area = w(34 - w)
area = 34w - w²
The maximum is at dA / dw = 0
Therefore,
34 - 2w = 0
2w = 34
w = 34 / 2
w = 17
l + w = 34
l + 17 = 34
l = 34 - 17
l = 17
area = 17² = 289 m²
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