Question

Jenny is building a rectangular garden around a tree in her yard. The southwest corner of the garden will be 2 feet south and 3 feet west of the tree. The northeast corner of the garden will be 1 foot north and 4 feet east of the tree. If jenny paves a path around the garden that is uniformly 3 feet wide, then what is the area of the path?

Answer 1

To find the area of the path, calculate the area of the outer rectangle and subtract the area of the inner rectangle (the garden). The area of the path is 18 square feet.

Step-by-step explanation:

To find the area of the path, we need to calculate the area of the outer rectangle and subtract the area of the inner rectangle (which represents the garden).

First, let's find the dimensions of the outer rectangle. The southwest corner of the garden is 2 feet south and 3 feet west of the tree, and the northeast corner of the garden is 1 foot north and 4 feet east of the tree.

The length of the outer rectangle is 2 + 1 = 3 feet, and the width is 3 + 4 = 7 feet.

The area of the outer rectangle is 3 * 7 = 21 square feet.

Now, let's find the dimensions of the inner rectangle (the garden). Since the width of the path is uniformly 3 feet, we can subtract 2 * 3 = 6 feet from both dimensions of the outer rectangle.

The length of the inner rectangle is 3 - 6 = -3 feet, and the width is 7 - 6 = 1 foot.

However, we can't have negative measurements for length or width. So we can take the absolute value, which gives us a length of 3 feet and a width of 1 foot.

The area of the inner rectangle is 3 * 1 = 3 square feet.

Now, to find the area of the path, we subtract the area of the inner rectangle from the area of the outer rectangle: 21 - 3 = 18 square feet.