# 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?

Feb 27, 2017

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 $A = w \times l$

Therefore:

The area of the outer rectangle is:

${A}_{1} = 24 \times 42 = 1008 s q f t$

The width of the inner rectangle is: $24 - 2 \frac{1}{2} - 2 \frac{1}{2} = 19 f t$
The length of the inner rectangle is $42 - 2 \frac{1}{2} - 2 \frac{1}{2} = 37 f t$

Therefore the area of the inner rectangle is:

${A}_{2} = 19 \times 37 = 703 s q f t$

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

${A}_{b} = 1008 - 703 = 305 s q f t$