A gardener is planning to construct a fence around a rectangular garden. The scale drawing is shown in the 𝑥𝑦-plane, where the garden is represented by a 4-inch by 6-inch rectangle. Each side of the garden is 20 times the corresponding side of the rectangle in the scale drawing. How many feet of fencing does the gardener need to construct the fence?Responses20 feetAnswer A: 20 feetA 3313 feetAnswer B: 33 and one third feetB40 feetAnswer C: 40 feetC400 feet
Question
A gardener is planning to construct a fence around a rectangular garden. The scale drawing is shown in the 𝑥𝑦-plane, where the garden is represented by a 4-inch by 6-inch rectangle. Each side of the garden is 20 times the corresponding side of the rectangle in the scale drawing. How many feet of fencing does the gardener need to construct the fence?Responses20 feetAnswer A: 20 feetA 3313 feetAnswer B: 33 and one third feetB40 feetAnswer C: 40 feetC400 feet
Solution
To determine the amount of fencing needed, follow these steps:
-
Identify the dimensions of the garden in the scale drawing:
- The garden is represented by a 4-inch by 6-inch rectangle.
-
Determine the actual dimensions of the garden:
- Each side of the garden is 20 times the corresponding side of the rectangle in the scale drawing.
- Actual length = 4 inches * 20 = 80 inches.
- Actual width = 6 inches * 20 = 120 inches.
-
Convert the dimensions from inches to feet:
- There are 12 inches in a foot.
- Actual length in feet = 80 inches / 12 = 6.67 feet (approximately).
- Actual width in feet = 120 inches / 12 = 10 feet.
-
Calculate the perimeter of the garden:
- Perimeter = 2 * (length + width).
- Perimeter = 2 * (6.67 feet + 10 feet) = 2 * 16.67 feet = 33.34 feet.
-
Round the perimeter to the nearest option provided:
- The closest option to 33.34 feet is 33 and one third feet.
Therefore, the gardener needs 33 and one third feet of fencing.
Answer B: 33 and one third feet
Similar Questions
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 27ft long and 20ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.)
Samantha is building a rectangular garden with a fence around it. If the length of the garden is 15𝑚 and the width is 10𝑚, what is the total length of the fence required?150𝑚300𝑚50𝑚
Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he has 80 feet of fencing to go around it, what dimensions will give him the maximum area in the garden?
A farmer wishes to put a fence diagonally across a rectangular field. He does not have time to measure the diagonal but already knows the sides of the existing field are 500 m by 1200 m. How much fencing will he need to buy?
A fence is to be built to enclose a rectangular area of 210 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 13 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.