Question

Jhanvi wants to make a rectangular park for children and others to play. The area of the park remains unchanged if its length is increased by 7 m and breadth is decreased by 3 m unit. Its area remains unaffected if the length is decreased by 7m and breadth is increased by 5m. Find the dimension of the park.

Answer 1

Solution:-
Let the Length and Breadth of the rectangular park be 'L' and 'B' respectively.
Area of rectangular park = (L × B) sq. units
Case 1:
Area of park remains unchanged if its length is increased by 7 m and breadth is decreased by 3m.
⇒ (L+7) (B-3) = (L × B) sq. units
⇒ LB - 3L + 7B - 21 = LB
⇒ - 3L + 7B - 21 = 0
⇒ - 3L + 7B = 21 .....(1)

Case 2: 
Area of the park remains unaffected if the length is decreased by 7 m and breadth is increased by 5 m.
(L - 7) (B + 5) = (L × B) sq. units
⇒ LB + 5L - 7B - 35 = LB
⇒ 5L - 7B - 35 = 0
⇒ 5L - 7B = 35 ....(2)
Adding (1) and (2), we get
⇒ - 3L + 7B = 21
       5L - 7B = 35 
_______________
       2L  = 56
L = 28 m
⇒ Putting L = 28 in the eq.(1)
⇒ (- 3 × 28) + 7B = 21
⇒ - 84 + 7B = 21
⇒ 7B = 21 + 84
⇒ 7B = 105 
⇒ B = 105/7
B = 15 m
So, Length = 28 m and Breadth = 15 m
Answer