A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 3 meters, the new total area of the garden will be 81 square meters. Find the length of each side of the original garden.
Responses
5m
5m - no response given
12m
12m - incorrect
3m
3m - no response given
6m
3 answers
6m
explain
Let x be the length of each side of the original garden.
The area of the original garden is x^2.
When each side is increased by 3 meters, the new total area is (x+3)^2 = x^2 + 6x + 9.
Given that the new total area is 81 square meters, we have:
x^2 + 6x + 9 = 81
x^2 + 6x - 72 = 0
(x+12)(x-6) = 0
This equation gives us two possible solutions for x: x = -12 or x = 6. Since the length of a side can't be negative, the correct side length is x = 6 meters.
The area of the original garden is x^2.
When each side is increased by 3 meters, the new total area is (x+3)^2 = x^2 + 6x + 9.
Given that the new total area is 81 square meters, we have:
x^2 + 6x + 9 = 81
x^2 + 6x - 72 = 0
(x+12)(x-6) = 0
This equation gives us two possible solutions for x: x = -12 or x = 6. Since the length of a side can't be negative, the correct side length is x = 6 meters.