Q14 of 37 Page 35

The perimeter of a rectangle is 240cm. If the length is decreased by 10% and its breadth is increased by 20% we get the same perimeter. Find the length and breadth of the rectangle.

Let the dimensions of the rectangle are

length = x cm


breadth = y cm


Given perimeter = 240 cm


⇒ 2(x + y) = 240


⇒ x + y = 120 ……(i)


If the length is decreased by 10% and breadth is increased by 20% then the new dimensions are








Perimeter = 240 cm




Divide each term with 3


⇒ 3x + 4y = 400 ……(ii)


Multiply equation (i) with 3 and subtract from (ii)


y = 40


Put y = 40 in (i)


x = 80


Therefore,


Required length and breadth of the rectangle are


Length = x = 80 cm


Breadth = y = 40 cm.


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