Question 112

The perimeter of a rectangular plot is 48 m and area is 108 m2. The dimensions of the plot are

Solution

Let the length of the plot be $$l$$ and breadth be $$b$$

=> Perimeter of rectangular plot = $$2(l + b) = 48$$

=> $$l + b = 24$$

Area of plot = $$lb = 108$$

=> $$l (24 - l) = 108$$

=> $$l^2 - 24l + 108 = 0$$

=> $$l^2 - 6l - 18l + 108 = 0$$

=> $$l(l-6) - 18(l-6) = 0$$

=> $$l = 6, 18$$

When $$l = 6$$ => $$b = 18$$

and when $$l = 18$$ => $$b = 6$$

=> Dimensions of the plot are 18 m and 6 m.

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