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. Its area will be increased by 164 units if its length is increased by 2 units and breadth is increased by 2 units. Find the dimensions of the park.
Answers
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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