Two rectangles are of same area equal to 480 square cm. They differ in lengths by 6 cm and breadths by 4 cm. What is the difference in their perimeters?

Explanation

Let the dimensions be (L, B) and (L-6, B+4). Area LB = 480 and (L-6)(B+4) = 480. Expanding gives 4L - 6B - 24 = 0 \implies 2L - 3B = 12. Substitute B = \frac{480}{L}: 2L - \frac{1440}{L} = 12 \implies 2L^2 - 12L - 1440 = 0 \implies (L-30)(L+24) = 0. Thus, L=30, B=16 with a perimeter of 2(30+16)=92. The second rectangle is 24 \times 20 with a perimeter of 2(24+20)=88. Difference = 92-88 = 4\text{ cm}.

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