Given : Shanta WANTS to make a rectangular park for children to PLAY.

The area of the park is increased by 75 square units if its length is decreased by 5 units and breadth is increased by 5 units.

area will be increased by 164 units if its length is increased by 2 units and breadth is increased by 2 units.

To Find :   the dimensions of the park.

Solution:

the dimensions of the park.

Length = L  and Breadth  = B

Area =  LB

The area of the park is increased by 75 square units if its length is decreased by 5 units and breadth is increased by 5 units.

=>   LB + 75  = (L - 5) (B + 5)

=> LB + 75 = LB  + 5L - 5B -  25

=> 5L - 5B = 100

=> L - B = 20

area will be increased by 164 units if its length is increased by 2 units and breadth is increased by 2 unit

=> LB + 164 = ( L + 2)(B + 2)

=>   LB + 164 =  LB + 2L + 2B + 4

=> L  + B  = 80

L  + B  = 80

L - B = 20

=> L = 50

    B = 30

Area = 50 * 30  = 1500  sq units

the dimensions of the park.  = Length 50 unit and Breadth = 30 units

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