A rectangular swimming pool is 10m wide and 15m long. The pool is surrounded by a deck of uniform width, whose area is equal to the area of the pool. How wide is the deck?
1500 sq cm
So the pool plus the deck is twice the area of the pool ...
(10+2w)(15+2w) = 2(10*15)
To determine the width of the deck, we should first calculate the area of the pool and then use that information to find the width of the deck.
The area of the pool can be found by multiplying its length by its width, which gives us:
Area of the Pool = Length × Width = 15m × 10m = 150m²
Let's assume the width of the deck is denoted by "w" meters.
Now, the total area of the pool and the deck combined can be calculated by adding the area of the pool to the combined area of the deck.
Area of the Pool + Area of the Deck = Total Area of the Pool and Deck
150m² + Area of the Deck = Total Area of the Pool and Deck
Since the problem statement states that the area of the deck is equal to the area of the pool, we can write:
150m² + 150m² = Total Area of the Pool and Deck
300m² = Total Area of the Pool and Deck
The total area of the pool and deck is equal to the length of the pool (including the deck) multiplied by its width (including the deck). So, we can write:
Total Area of the Pool and Deck = (Length + 2w) × (Width + 2w)
Substituting the known values, we get:
300m² = (15m + 2w) × (10m + 2w)
Now, we need to solve this quadratic equation to find the value of "w."
Expanding the equation gives:
300m² = 150m² + 30mw + 20mw + 4w²
Combining like terms:
300m² = 180m² + 50mw + 4w²
Rearranging the equation:
0 = 120m² + 50mw + 4w²
Now, we have a quadratic equation in the form ax² + bx + c = 0, where:
a = 4
b = 50m
c = 120m²
Solving this equation will give us the value of "w," which represents the width of the deck.
(10 + 2 w) (15 + 2w) = 2 * 10 * 15
150 + 50 w + 4 w^2 = 300
2 w^2 + 25 w - 75 = 0
(2 w - 5) (w + 15) = 0
2 w - 5 = 0
w + 15 = 0