Q2 of 227 Page 79

Formulate the following problems as a pair of equations, and hence find their solutions:

In a rectangle, if the length is increased and the breadth is reduced each by 2 cm then the area is reduced by 28 cm2. If the length is reduced by 1 cm and the breadth increased by 2 cm , then the area increases by 33 cm2. Find the area of the rectangle.

Let length be l and breadth be b.


Then the first condition is


(l + 2) (b – 2) = lb – 28


⇒ lb – 2l + 2b – 4 – lb + 28 = 0


⇒ – 2l + 2b + 24 = 0


⇒ – l + b + 12 = 0


The second condition is


(l – 1) (b + 2) = lb + 33


⇒ lb + 2l – b – 2 – lb – 33 = 0


⇒ 2l – b – 35 = 0


For cross multiplication method, we write the coefficients as



Hence, we get = =


⇒ = =


⇒ = =


⇒ l = = 23


⇒ b = = 11


∴ Area of rectangle= l × b = 23 × 11 = 253 cm2


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