The length of a rectangle is 4 m more than the width. The area of the rectangle is 45 square meters. Find the length and width.
L = W+4
L * W = (W+4) * W = 45
W = 5
Solve for L.
2.5
To find the length and width of the rectangle, we can use the given information and solve for the unknowns.
Let's assume that the width of the rectangle is 'x' meters.
According to the problem, the length of the rectangle is 4 meters more than the width. So, the length can be represented as 'x + 4' meters.
The area of a rectangle is given by the formula: Area = Length * Width.
Given that the area is 45 square meters, we can set up an equation using the values we have:
x * (x + 4) = 45
Now, we can solve for 'x' by simplifying and solving the resulting quadratic equation:
x^2 + 4x = 45
Rearranging the equation:
x^2 + 4x - 45 = 0
To solve this quadratic equation, we can factor or use the quadratic formula. Factoring the equation, we determine that:
(x - 5)(x + 9) = 0
Setting each factor equal to zero and solving for 'x', we find two possible values:
x - 5 = 0 or x + 9 = 0
Solving each equation:
x = 5 or x = -9
Since the width of a rectangle cannot be negative, we can ignore the solution x = -9. Therefore, the width of the rectangle is 5 meters.
To find the length, we substitute the width value back into the expression for the length:
Length = Width + 4 = 5 + 4 = 9 meters
Hence, the length of the rectangle is 9 meters and the width is 5 meters.