Question
When the breadth of a rectangle is reduced by 4cm
(keeping the length constant), its area reduces by 72 cm2 and when the length is reduced by 4cm (keeping the length constant), its area reduces by 64cm2. What is the perimeter of the rectangle? (in cm)Solution
Let the length of the rectangle be l cm and breadth be b cm Area = lb Case 1 - Length = l and Breadth = b - 4 Area = l(b - 4) = lb - 4l So, lb - {lb - 4l} = 72 4l = 72, therefore l = 18 cm Case 2 - Length = (l - 4) and Breadth = b Area = (l - 4)b = lb - 4b So, lb - {lb - 4b} = 64 4b = 64, therefore b = 16 cm Now, Perimeter = 2 (l + b) = 2 (18 + 16) = 2 x 34 = 68 cm
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