Sita Devi wants to make a rectangular pond on the roadside for the purpose of providing drinking water for street animals the area of the pond will be decreased by 3 square feet if its length is decreased by 2 fit and Breadth is increase by 1 ft. its area will be increased by 4 square feet if the length is increased by 1 feet and breadth remain same find the dimension of the pond
Answers
Answer:
The dimension of the pond is 4 ft by 7 ft.
Step-by-step explanation:
Define x and y:
Let x be the length of the pond
Let y be the breadth of the pond
Find the area of the pond:
Area of the pond = Length x Breadth
⇒ Area of the pond = xy
If length is decreased by 2 ft and breadth increased by 1 ft
⇒ Area = (x - 2)(y + 1)
The area is decreased by 3 ft²
⇒ xy - (x - 2)(y + 1) = 3
⇒ xy - (xy + x - 2y - 2) = 3
⇒ xy - xy - x + 2y + 2 = 3
⇒ 2y - x - 1 = 0
If length is increased by 1 and the breadth remained the same:
⇒ Area = (x + 1)y
The area is increased by 4 ft²:
⇒ (x + 1)y - xy = 4
⇒ xy + y - xy = 4
⇒ y = 4 ft
Solve for x:
Sub y = 4 into 2y - x - 1 = 0
2(4) - x - 1 = 0
8 - x - 1 = 0
7 - x = 0
x = 7 ft
Answer: The dimension of the pond is 4 ft by 7 ft.
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