A family plans to surround their pool with a patio of constant width. The pool has an area of 150 square feet. The dimensions of the pool with the patio will be 15 feet by 20 feet. Find the dimensions of the pool.

The dimension of the pool is 10 ft by 15 ft.

Step-by-step explanation:

Let

a = width of the patio around the pool

The pool has an area of 150 ft². The dimension of the pool with the patio is 15 ft by 20 ft which also includes the a ft of the patio on each side. Therefore the dimension of the pool can be expressed as

(15 - 2a) (20 - 2a) = 150

300 - 30a - 40a + 4a² = 150

4a² - 70a + 300 - 150 = 0

4a² - 70a + 150 = 0

divide both sides by 2

2a² - 35a + 75 = 0

Find the numbers you can multiply that will give you 150 and also add that will give - 35. The numbers are - 30 and - 5.

2a² - 5a - 30a + 75 = 0

a (2a - 5) - 15 (2a - 5) = 0

(a - 15) (2a - 5) = 0

a = 15 or 5/2

Using a = 15 will make the width and length negative so we use 5/2

(15 - 2a) (20 - 2a) = 150

(15 - 2 (5/2)) (20 - 2 (5/2))

(15 - 5) (20 - 5)

10 * 15 = 150 ft².

The dimension of the pool is 10 ft by 15 ft.