the length of a playground id 6 meters less than 3 times its width. If the perimeter of the playground is 100 meters what is the lenght and width of the area to the nearest hundredth meter?
grahaping
y=3
Length is 6 less than 3xwidth so L=3W-6
Perimeter = L+L+W_W or 2L+2W
Perimeter is 100m so 2L+2W=100
You have 2 equations and 2 unknowns so you can solve it.
To solve this problem, let's assign variables to the length and width of the playground:
Let L be the length of the playground.
Let W be the width of the playground.
According to the given information:
L = 3W - 6 (Length is 6 meters less than 3 times width)
Perimeter = 100 (The sum of all sides is 100 meters)
The perimeter of a rectangle is calculated by adding the lengths of all four sides:
Perimeter = 2(L + W)
Substituting the values we know:
100 = 2(L + W)
Now, let's solve this system of equations to find the length and width.
Substitute the value of L from the first equation into the second equation:
100 = 2((3W - 6) + W)
Simplify:
100 = 2(4W - 6)
Distribute the 2:
100 = 8W - 12
Move the constant term to the other side:
8W = 100 + 12
8W = 112
Divide by 8:
W = 112 / 8
W = 14
Now, substitute the value of W back into the first equation to find the length:
L = 3W - 6
L = 3(14) - 6
L = 42 - 6
L = 36
Therefore, the length of the playground is approximately 36 meters and the width is approximately 14 meters.