Geometry

Jake is looking to buy some fence for his square garden. He will need enough fencing for the radish, carrots, lettuce, and his front gate. Place answers in the form of a radical. The garden has: - 3 carrot sections each = 27 ft^2 - 4 radish sections each = 12 ft^2 - 1 lettuce section = 48 ft^2 - 1 front gate section 1. How much fence will he need to make a perimeter around the carrot section?

Step-by-step solution with explanation

Final Answer

ft

Step-by-step solution

1

Find the area of one carrot section

Each carrot section is a square with an area of 27 square feet. We are told this directly in the problem.
2

Find the side length of one carrot square

Since the section is a square, we find the side length by taking the square root of the area. So the side length is ft.
3

Simplify the radical for side length

We simplify by finding a perfect square factor. Since , we get ft per side.
4

Find perimeter of one carrot square

The perimeter of a square is 4 times the side length. One carrot section needs ft of fencing.
5

Find total fencing for all 3 carrot sections

There are 3 carrot sections, each needing ft of fencing. Multiply to get the total for all carrot sections.

Understanding this problem

Learning Insight

For any square, area and side length are connected by , so . Simplifying radicals works by pulling out perfect square factors — this keeps answers exact instead of using rounded decimals.

Quick Tip

To simplify , ask: what is the biggest perfect square that divides into ? For 27, that's 9. Pull it out as a whole number: .

Common Mistake

Students often forget there are 3 carrot sections and only calculate the perimeter of one section, giving instead of the correct total of ft.