Jenna is planting four circular gardens. She is planting one garden each for tomatoes, carrots, cabbage, and strawberries. Each garden will have a fence around it to keep rabbits out. The tomato, carrot, and cabbage gardens will all be the same size. Since Jenna loves strawberries, the strawberry garden will be larger. It will use the same amount of fencing as the other three gardens combined. She used a total of about 113.04 feet of fencing material.

Question

Jenna is planting four circular gardens. She is planting one garden each for tomatoes, carrots, cabbage, and strawberries. Each garden will have a fence around it to keep rabbits out. The tomato, carrot, and cabbage gardens will all be the same size. Since Jenna loves strawberries, the strawberry garden will be larger. It will use the same amount of fencing as the other three gardens combined. She used a total of about 113.04 feet of fencing material.

Answer 1

Let x be the radius of the tomato, carrot, and cabbage gardens.

The circumference of a circle is given by 2πr, where r is the radius.

So, the fencing needed for each of the tomato, carrot, and cabbage gardens is 2πx.

The circumference of the strawberry garden is 2π(2x) = 4πx.

The total fencing needed is:
2(2πx) + 4πx = 8πx.

Given that the total fencing used is about 113.04 feet, we have:
8πx = 113.04.

Dividing both sides by 8π to solve for x:
x = 113.04 / (8π) ≈ 4.5 feet.

Therefore, the radius of each of the tomato, carrot, and cabbage gardens is approximately 4.5 feet, and the radius of the strawberry garden is 2 times that, so 9 feet.