there is a swimming pool, 3 meters in width and 4 meters in length. the owner wants to built a uniform deck around the swimming pool which is 3 times of the area of the pool. what's the width of the deck?
If the area of the deck is 3 times the pool, then the total area of pool+deck is 4 times just the pool.
If the width of the deck is w, you need
(3+2w)(4+2w) = 4(3)(4)
36
To find the width of the deck, we first need to calculate the area of the swimming pool.
Area of the swimming pool = length × width
= 4 meters × 3 meters
= 12 square meters
Next, we need to find the area of the desired deck, which is three times the area of the pool.
Area of the deck = 3 times the area of the pool
= 3 × 12 square meters
= 36 square meters
Since the deck will surround the pool uniformly, we can find the width of the deck by subtracting the dimensions of the pool from the overall dimensions of the deck.
Let the width of the deck be x.
Overall width of the deck = (width of the pool + 2 × width of the deck)
= (3 meters + 2x)
Overall length of the deck = (length of the pool + 2 × width of the deck)
= (4 meters + 2x)
The area of the deck can be calculated by multiplying the overall width and length of the deck.
Area of the deck = Overall width × Overall length
= (3 meters + 2x) × (4 meters + 2x)
= 12 + 14x + 4x^2
Since the area of the deck is equal to 36 square meters, we can set up the equation:
12 + 14x + 4x^2 = 36
Simplifying the equation:
4x^2 + 14x + 12 = 36
4x^2 + 14x - 24 = 0
Now we can solve this quadratic equation by factoring or using the quadratic formula. After finding the value of x, we can determine the width of the deck.
To find the width of the deck, we first need to calculate the area of the swimming pool and then calculate the desired area of the deck.
The area of the swimming pool can be calculated by multiplying its width by its length:
Area of swimming pool = width x length = 3 meters x 4 meters = 12 square meters.
Now, since the owner wants the deck to have an area three times that of the swimming pool, we can calculate the desired area of the deck:
Desired area of deck = 3 x Area of swimming pool = 3 x 12 square meters = 36 square meters.
To find the width of the deck, we need to determine the dimensions of the overall rectangular shape that includes both the pool and the deck. Let's assume that the width of the deck is x meters.
Considering this, the overall width of the deck and the pool will be:
Overall width = pool width + 2 x deck width = 3 meters + 2x.
Similarly, the overall length will be:
Overall length = pool length + 2 x deck width = 4 meters + 2x.
To find the width of the deck, we need to solve for x by creating an equation using the given information.
We know that the area of the overall shape (pool + deck) is equal to the desired area of the deck, so we can write the following equation:
Overall width x Overall length = Desired area of deck.
Substituting the values we calculated:
(3 meters + 2x) x (4 meters + 2x) = 36 square meters.
To solve this equation, we can multiply out the binomials:
12 meters^2 + 10x + 2x^2 = 36 square meters.
Rearranging the equation to set it equal to zero:
2x^2 + 10x + 12 - 36 = 0.
Combining like terms:
2x^2 + 10x - 24 = 0.
Now, to solve this quadratic equation, we can either factor it or use the quadratic formula. Upon factoring, we get:
(x + 6)(2x - 4) = 0.
Setting each factor equal to zero and solving for x, we find two possible solutions:
x + 6 = 0 or 2x - 4 = 0.
For x + 6 = 0, x = -6, but since we are looking for a positive width, this is not a valid solution.
For 2x - 4 = 0, x = 2.
Therefore, the width of the deck is 2 meters.