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A rectangular garden measures 20 ft by 37 ft Surrounding (end bordering) the garden is a path 2 f wide. Find the area of this path. Be sure to incuide the correct unit in your answer.

Ask by Barker Gough. in the United States
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The area of the path is 244 square feet.

Solution

**Step 1: Determine the dimensions of the outer rectangle (garden + path).** The garden has dimensions \(20 \text{ ft}\) by \(37 \text{ ft}\). Since the path is \(2 \text{ ft}\) wide on every side, the length and width of the outer rectangle are increased by \(2 \times 2 = 4 \text{ ft}\) each. \[ \text{New width} = 20 + 4 = 24 \text{ ft} \] \[ \text{New length} = 37 + 4 = 41 \text{ ft} \] **Step 2: Calculate the area of the outer rectangle.** \[ \text{Area}_{\text{outer}} = 24 \times 41 = 984 \text{ ft}^2 \] **Step 3: Calculate the area of the garden (inner rectangle).** \[ \text{Area}_{\text{garden}} = 20 \times 37 = 740 \text{ ft}^2 \] **Step 4: Find the area of the path by subtracting the area of the garden from the area of the outer rectangle.** \[ \text{Area}_{\text{path}} = \text{Area}_{\text{outer}} - \text{Area}_{\text{garden}} = 984 - 740 = 244 \text{ ft}^2 \] **Final Answer:** The area of the path is \(244 \text{ ft}^2\).

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To find the area of the path surrounding the garden, first calculate the dimensions of the outer rectangle formed by the garden and the path. The garden is 20 ft by 37 ft, and with a 2 ft path on each side, the dimensions become (20 + 2 + 2) ft by (37 + 2 + 2) ft, which is 24 ft by 41 ft. Now, calculate the area of the outer rectangle: Area = Length x Width = 24 ft x 41 ft = 984 sq ft. Next, calculate the area of the garden itself: Area of the garden = 20 ft x 37 ft = 740 sq ft. Finally, the area of the path is: Area of the path = Area of the outer rectangle - Area of the garden = 984 sq ft - 740 sq ft = 244 sq ft. So, the area of the path is **244 sq ft**.

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