"central park is 5 meters longer than it is wide. The area is 2250 square meters. find the length of the park"
width --- x
length --- x+5
x(x+5) = 2250
x^2 + 5x - 2250 = 0
(x - 45)(x+50) = 0
x= 45 or x = -50, last part is silly
length is 50, width = 45
check: area = 45(50) = 2250
To find the length of the park, we first need to set up an equation using the given information. Let's assume the width of the park is x meters.
According to the problem, the park is 5 meters longer than it is wide. So, the length of the park would be x + 5 meters.
The area of a rectangle is given by the formula: Area = Length × Width.
Given that the area is 2250 square meters, we can write the equation as:
2250 = (x + 5) × x
Now, we can solve this equation to find the value of x. Let's expand and simplify the equation:
2250 = x^2 + 5x
Rearranging the equation to bring all the terms to one side:
x^2 + 5x - 2250 = 0
To solve this quadratic equation, we can factorize it or use the quadratic formula. Factoring may not be straightforward in this case since the coefficients are large, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 5, and c = -2250. Substituting these values into the quadratic formula:
x = (-5 ± √(5^2 - 4(1)(-2250))) / (2(1))
Simplifying further:
x = (-5 ± √(25 + 9000)) / 2
x = (-5 ± √9025) / 2
x = (-5 ± 95) / 2
Now, we have two possible values for x:
x₁ = (-5 + 95) / 2 = 90/2 = 45
x₂ = (-5 - 95) / 2 = -100/2 = -50
Since we are dealing with dimensions, the width cannot be negative. Therefore, we discard the value of x = -50.
Hence, the width of the park is 45 meters.
To find the length, we add 5 to the width:
Length = Width + 5 = 45 + 5 = 50 meters
Therefore, the length of the park is 50 meters.