If the perimeter of a rectangle is 60m and the area is 225m^2 what is the length of the rectangle?
L * w = 225
2 L + 2 w = 60 so L + w = 30 and w = 30-L
L (30-L) = 225
30 L - L^2 = 225
L^2 -30 L + 225 = 0
(L-15)(L-15) = 0
L = 15 meters
Thank you for your help! :)
You are welcome.
To find the length of the rectangle, we can use the given information about its perimeter and area.
Let's assume the length of the rectangle is L and the width is W.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. For a rectangle, since opposite sides are equal, we can calculate the perimeter as:
Perimeter = 2L + 2W
From the given problem, we know that the perimeter is 60m. So we can write the equation as:
60 = 2L + 2W
Similarly, the area of a rectangle is calculated by multiplying the length and width:
Area = L * W
From the given problem, we know that the area is 225m^2. So we can write the equation as:
225 = L * W
We now have a system of two equations with two unknowns (L and W):
Equation 1: 60 = 2L + 2W
Equation 2: 225 = L * W
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.
From Equation 1, we can isolate W:
2W = 60 - 2L
W = 30 - L/2
Substitute this value in Equation 2:
225 = L * (30 - L/2)
225 = L * 30 - L^2/2
450 = 30L - L^2/2
2L^2 - 60L + 900 = 0
L^2 - 30L + 450 = 0
We now have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
L = (-(-30) +/- sqrt((-30)^2 - 4(1)(450))) / (2(1))
L = (30 +/- sqrt(900 - 1800)) / 2
L = (30 +/- sqrt(-900)) / 2
Since the square root of a negative number is not real, it means that there are no real solutions for L. Therefore, it is not possible to determine the length of the rectangle based on the given information.