The length of a rectangle is 3 meters more than its width.If the area is 108 sqaure meters What are the length and width?
L=Lenght
W=Width
L=W+3
A=L*W
108=(W+3)*W
108=W^2+3W
W^2+3W-108=0
Solutions of this equation is:
-12 and 9
Lenght can't be negative,so W=9m
L=W+3=9+3=12m
L=12m W=9m
A=12*9=108m^2
To find the length and width of the rectangle, you can set up an equation based on the given information.
Let's assume that the width of the rectangle is represented by 'x' meters. Since the length is 3 meters more than the width, it can be represented as 'x + 3' meters.
The formula for the area of a rectangle is length multiplied by width:
Area = Length × Width
We know that the area is given as 108 square meters. Substituting the values into the equation:
108 = (x + 3) × x
Now, we can solve this quadratic equation to find the values of 'x' (width) and 'x + 3' (length).
To solve for x, expand the equation:
108 = x^2 + 3x
Rearrange the equation, so that it is equal to zero:
x^2 + 3x - 108 = 0
Now, we can either factor this quadratic equation or use the quadratic formula to find the value of 'x'. I will use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 3, and c = -108. Plug these values into the formula:
x = (-3 ± √(3^2 - 4(1)(-108))) / (2(1))
Simplifying further:
x = (-3 ± √(9 + 432)) / 2
x = (-3 ± √441) / 2
Now, calculate the square root:
x = (-3 ± 21) / 2
This gives us two potential values for 'x':
x₁ = (-3 + 21) / 2 = 9
x₂ = (-3 - 21) / 2 = -12
Since we're dealing with lengths, the width cannot be negative. Therefore, the width (x) is 9 meters.
Now, substitute this value back into the length equation:
Length = Width + 3
Length = 9 + 3
Length = 12 meters
So, the length of the rectangle is 12 meters, and the width is 9 meters.