Using the formula for the perimeter and area of rectangle, the dimensions are: Length = 19 m; width = 9 m.
Perimeter = 2(length + width)
Area = (length)(width).
Let x represent the length and y the width, therefore:
2(x + y) = 56 --> eqn. 1
xy = 171 --> eqn. 2
Rewrote eqn. 1
x + y = 56/2
x = 28 - y
Substitute x = (28 - y) into eqn. 2
171 = (28 - y)y
171 = 28y - y²
171 - 28y + y² = 0
y² - 28y + 171 = 0
Factorize
(y - 9)(y - 19)
y = 9 and y = 19
Therefore, the dimensions are: Length = 19 m; width = 9 m.
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