Question

A walled rectangular garden is 24 feet wide and 42 feet long. Flowers are to be planted along the outside edges of the garden to form a border that is 2 1/2 (two and a half) feet wide all around. What will be the area of the border?

Answer 1

The area of the border is 20 square feet.

Explanation:

There are two rectangles in this problem. (See picture).

One is a rectangle covering the entire garden. The area of this we can call `A_1`.

The other rectangle is the space remaining in the garden inside the border of flowers. This area we can call `A_2`

The area of the border is the difference between the area of these two rectangles. This area we can call `A_b` and can be calculated as: `A_b = A_1 - A_2`

The formula for the area of a rectangle is `A = w xx l`

Therefore:

The area of the outer rectangle is:

`A_1 = 24 xx 42 = 1008 sq ft`

The width of the inner rectangle is: `24 - 2 1/2 - 2 1/2 = 19ft`
The length of the inner rectangle is `42 - 2 1/2 - 2 1/2 = 37ft`

Therefore the area of the inner rectangle is:

`A_2 = 19 xx 37 = 703 sq ft`

The area of the border is the difference between the area of these two rectangles:

`A_b = 1008 - 703 = 305 sq ft`