FWT wrote:A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.
Start by drawing a picture:
+--------------+
| |
| +--------+ |
| | | |
| | | |
| +--------+ |
| |
+--------------+
Since the length of the pool (the inner rectangle) is defined in terms of the width, pick a variable for the width, create an expression for the length, and label:
+--------------+
| |
|--+--------+ |
| | | |
|w | | |
|--+--------+ |
| | 2w | |
+--------------+
What expression will represent the area of the pool? (Hint: Multiply the length and width!)
You are given that the walkway (the outer rectangle) is 2 units wide. If the width of the pool is "w", and if the walkway adds two units to either end of that, what expression then represents the width of the outer rectangle? Use the same reasoning to find an expression for the length of the outer rectangle.
You are given the area of the outer portion, so multiply the "width" and "length" expressions for the whole area, subtract the expression for the inner area, and simplify to find an expression for just the outer portion. Then set this equal to the given "walkway only area" value, and
solve the resulting equation.
Remember to interpret your solution(s) within the context of the exercise. For instance, you can't have negative lengths.