The length of a car park is 12m longer than its with. The area of the car park is 64m². Find the dimensions of the car park?
L = W + 12
A = L ∙ W = 64
( W + 12 ) ∙ W = 64
W² + 12 W = 64
Subtract 64 to both sides
W² + 12 W - 64 = 0
Try to solve this equation.
The solutions are:
W = - 16 and W = 4
Width can not be negative so W = 4 m
L = W + 12 = 4 + 12 = 16 m
A = L ∙ W = 16 ∙ 4 = 64 m²
W =
This is true if a car park is rectangular.
To find the dimensions of the car park, we can set up a system of equations using the given information.
Let's denote the width of the car park as "w" (in meters). According to the problem, the length of the car park is 12 meters longer than its width, so the length can be represented as "w + 12" (in meters).
The area of a rectangle is found by multiplying its length by its width. Thus, we have the following equation:
Area = Length × Width
64 = (w + 12) × w
Now, let's solve this equation to find the dimensions of the car park:
64 = w^2 + 12w
Rearranging the equation, we have:
w^2 + 12w - 64 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use factoring:
(w + 16)(w - 4) = 0
Setting each factor equal to zero, we have two possible solutions:
w + 16 = 0 or w - 4 = 0
Solving for "w" in each equation, we get:
w = -16 or w = 4
Since the width of the car park cannot be negative, we discard the solution w = -16.
Therefore, the width of the car park is w = 4 meters.
To find the length, we can substitute this value back into the equation for the length:
Length = Width + 12
Length = 4 + 12
Length = 16 meters
So, the dimensions of the car park are 4 meters (width) and 16 meters (length).