The sum of the length and the breadth of a rectangle is 240 cm. If the length is
decreased by 20% and the breadth is increased by 10% the perimeter remains the
same. Find the dimensions of the rectangle.
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〚 Sum of the length and the breadth is 240 cm 〛
So,
➜ x + y = 240
➜ x = 240 - y ------ (1)
〚 Also given that , when the length is decreased by 20% and the breadth is increased by 10% the perimeter remains the same 〛
Length is decreased by 20%
➜
➜
➜
➜
Breadth is increased by 10%
➜
➜
➜
➜
➠ 2(length + breadth)
➜ 2(length + breadth)
➜ 2(240)
➜ 480 cm
➜ 2(length + breadth)
➜
➜
➜ cm ----- (2)
➜
➜
➜ cm
Given that perimeter remains unchanged
So,
➜
➜
➜
➜
➜
➜
➨
➜ x = 240 - y
➜ x = 240 - 160
➨ x = 80
Therefore the length and breadth of rectangle is 80 cm & 160 cm respectively
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Additional information
Properties of rectangle
Let the length of rectangle be "x"
Let the breadth of rectangle be "y"
〚 Sum of the length and the breadth is 240 cm 〛
So,
➜ x + y = 240
➜ x = 240 - y ------ (1)
〚 Also given that , when the length is decreased by 20% and the breadth is increased by 10% the perimeter remains the same 〛
Length is decreased by 20%
➜
➜
➜
➜
Breadth is increased by 10%
➜
➜
➜
➜
➠ 2(length + breadth)
➜ 2(length + breadth)
➜ 2(240)
➜ 480 cm
➜ 2(length + breadth)
➜
➜
➜ cm ----- (2)
➜
➜
➜ cm
Given that perimeter remains unchanged
So,
➜
➜
➜
➜
➜
➜
➨
Hence breadth of rectangle is 160 cm
➜ x = 240 - y
➜ x = 240 - 160
➨ x = 80
Hence length of rectangle is 80 cm
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