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Question
A large square is made by arranging a small square surrounded by four congruent rectangles as shown in the following figure. If the perimeter of each of the rectangle is 16 cm, find the area of the large square.
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Solution
Let the length and breadth of rectangle be l and b, respectively.
It is given that, perimeter of one rectangle = 16 cm2
⇒ 2(l + b) = 16 ...[∵ Perimeter of rectangle = 2(l + b)]
⇒ l + b = 8 cm
Since, the side of larger square is (l + b).
Hence, area = (side)2 = (l + b)2 = (8)2 = 64 cm2
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