You have a pool that measure 15 yards by 10 yards. You want to build a deck around all four sides of the pool and you want to increase the total area to 250 square yards. What is the width of the deck?
Total Area= 4w^2 + 2*15w+2*10w=250
2w^2+25w-125=0
w=(-25+-sqrt(625+1000))/4
w=(-25+-sqr(1625)/4=15.3/4
check:
area=4(15.3/4)^2 + 50(15.3/4)=
=250
To solve this problem, we need to first calculate the area of the pool and then determine the area of the deck. Finally, we can find the width of the deck by subtracting the pool area from the desired total area and dividing the result by the sum of the pool's length and width.
1. Calculate the area of the pool:
The pool measures 15 yards by 10 yards, so the area is: 15 yards * 10 yards = 150 square yards.
2. Determine the area of the deck:
The desired total area is 250 square yards, and we already know the pool's area is 150 square yards. Therefore, the area of the deck is: 250 square yards - 150 square yards = 100 square yards.
3. Find the width of the deck:
Let's assume the width of the deck is x yards.
The area of the deck can be expressed as the sum of the areas on each side of the pool:
2 * (x yards * 15 yards) + 2 * (x yards * 10 yards) = 100 square yards.
Simplifying this equation gives: 30x + 20x = 100.
Combining the like terms, we have: 50x = 100.
Dividing both sides by 50, we get: x = 2 yards.
Therefore, the width of the deck should be 2 yards.