Question 37757
Let x = the width of the patio.
From the problem...
(length of the total area - patio)*(width of the total area - patio) = area of pool 150.
Since the patio borders the entire area we need to account for it twice.
So, our equation is...
(20-2x)(15-2x)= 150
FOIL...
300 - 70x + 4x^2 = 150
Subtract 150 from both sides...
150 - 70x + 4x^2 = 0
In standard form this becomes...
4x^2 -70x +150 = 0
This can be simplified by factoring out a 2...
2(2x^2 - 35x + 75) = 0
Then factor completely...
(2x^2 - 30x) - (5x +75) = 0
And...
2x(x - 15) -5(x - 15) = 0
With the result...
(x-15)(2x-5) = 0
So...
(x-15) = 0 or (2x-5) = 0
x = 15 or x = 2.5
Since the width of the entire area is 15, the width of the patio cannot be 15 so that eliminates x = 15 as a correct result.
So the width of the patio is 2.5 feet.
To find the dimensions of the pool we subtract our answer from the total length and width. Substitute answer in original equation.
20 - 2(2.5) = 20 - 5 = 15
and...
15 - 2(2.5) = 15 - 5 = 10
and...
15 * 10 = 150 (the total area of the pool.
So...
The pool is 15' x 10'
I hope this helps
Good Luck!