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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)

A 64 cm Correct Answer Incorrect Answer
B 68 cm Correct Answer Incorrect Answer
C 72 cm Correct Answer Incorrect Answer
D 56 cm Correct Answer Incorrect Answer
E None of these Correct Answer Incorrect Answer

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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