The local swimming pool is rectangular and the length is 5 feet more than twice the width If the area of the pool is 1375 square feet then what are the length and width of the pool
width ---- x
length ---- 2x+5
x(2x+5) = 1375
2x^2 + 5x - 1375 = 0
solve the quadratic
hint: it factors, but it may be just as fast to use the formula
To find the length and width of the pool, we can set up an equation based on the given information.
Let's say the width of the pool is represented by 'w'. According to the problem, the length is 5 feet more than twice the width, which can be written as:
Length = 2w + 5
The area of a rectangle is calculated by multiplying its length and width. In this case, the area of the pool is given as 1375 square feet:
Area = Length * Width
Substituting the values we have:
1375 = (2w + 5) * w
Now we need to solve this equation to find the value of 'w'.
1375 = 2w^2 + 5w (expanding)
Rearranging the equation to form a quadratic equation:
2w^2 + 5w - 1375 = 0
Now we can solve this quadratic equation to find the values of 'w'. The quadratic equation can be factored or solved using the quadratic formula:
w = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 2, b = 5, and c = -1375.
After solving this equation, you will find two values for 'w', one positive and one negative. Since the width of the pool cannot be negative, we can discard the negative solution.
Once you have found the value of 'w', you can substitute it back into the equation Length = 2w + 5 to find the length of the pool.