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?

1 Answer
smendyka
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 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#

enter image source here

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