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