The deck around a swimming pool has the same width all the way around. The perimeter of the pool is 50m. The outside perimeter of the deck is 74m. What is the width of the deck
If the length and width of the pool are L and W, and the width of the path is w, then
perimeter of the pool = 2(W+L)
perimeter of the outside = 2(W+2w + L+2w)
Difference between outside perimeter and the pool
=2(W+2w + L+2w) - 2(W+L)
=8w
So w=(74-50)/8=24/8=3 m
To find the width of the deck, we need to set up and solve an equation based on the given information.
Let's assume the width of the deck is represented by 'x'. Since the deck goes around the pool, the dimensions of the pool will be smaller when the deck is taken into account.
The perimeter of the pool is 50m. Since the width of the deck is the same on all sides, the length and width of the pool together will be (50 - 2x) meters. Subtracting 2x from 50 removes the width of the deck from both sides of the pool.
The outside perimeter of the deck is given as 74m. Considering that the deck goes around the pool, we can calculate the total length and width of the pool and the deck combined. The formula for the outside perimeter of the deck is given by 2*(length + width). In this case, the total length and width will be (50 - 2x) + (50 - 2x) = 2(50 - 2x), which equals 74m.
Now, we can set up the equation and solve for 'x':
2(50 - 2x) = 74
First, distribute the 2:
100 - 4x = 74
Then, subtract 100 from both sides:
-4x = -26
Finally, divide both sides by -4:
x = 6.5
Therefore, the width of the deck is 6.5 meters.