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.

The area of each smaller garden is about ___
square feet.

The area of the larger garden is about ____
square feet.

The area of the larger garden is ___
times larger than the area of the smaller garden.

Answer 1

254.34 square feet in the larger green

Explanation:

Tomato + carrot + cabbage + ( 3* carrot) =113.04 ft

1x+1x+1x+3 x= 113.04

6x= 113.04

x=113.04/6 = 18.84 feet of fence = circumference

The circumference of the tomato, carrot and cabbage gardens is 18.84 feet each. The circumference of the strawberry garden will be 3 times larger of 3x 18.84 = 56.52 feet.

With the circumference we can find the diameters, and with the diameters we can find the areas.

For the 3 small gardens, d= c/
`\pi`

d= 18.84 / 3.14

d=6 and the radius is 3 feet

Area =
`\pi`^2

A= 3.14 x 3 x 3= 28.26 square feet in each of the 3 small gardens

For the larger garden

d=6x3=18 feet and the radius is 9 feet

Area =
`\pi`^2

A= 3.14 x 9 x 9 = 254.34 square feet in the larger garden