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Question
In the following figure, a rectangle with perimeter 264 cm is divided into five congruent rectangles. Find the perimeter of one of the rectangles.
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Solution
Let l and b the length and breadth of each rectangle, respectively.
Given, perimeter of a rectangle = 264 cm
According to the figure,
4l + 5b = 264 ...(i)
And 2l = 3b ...(ii)
Put the value of 3b from equation (ii) in equation (i),
2(2l) + 5b = 264
⇒ 2 × 3b + 5b = 264
⇒ 6b + 5b = 264
⇒ 11b = 264
⇒ b = `264/11`
⇒ b = 24 cm
∴ `l = (3b)/2 = (3 xx 24)/2` = 36 cm
Hence, perimeter of the rectangle = 2(1 + b) = 2(36 + 24) = 120 cm.
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