A Rectangular garden has length twice its width. The perimeter of the garden is 54 m. What is its perimeter?
L = 2 W
P = 2 L + 2 W = 2 ( L + W )
P = 54
2 ( L + W ) = 54 Divide both sides by 2
L * W = 54 / 2
L + W = 27
Replace L = 2 W in this equation.
2 W + W = 27
3 W = 27 Divide both sides by 3
W = 27 / 3
W = 9 m
L = 2 W = 2 * 9 = 18 m
Proof:
P = 2 ( L + W ) = 2 ( 18 + 9 ) = 2 * 27 = 54 m
To find the perimeter of a rectangular garden, we need to know the values of its length and width. In this case, we are given that the garden's length is twice its width.
Let's assume the width of the garden is x meters.
Therefore, the length of the garden would be 2x meters, as it is twice the width.
The formula for the perimeter of a rectangle is:
Perimeter = 2(Length + Width)
Plugging in the values we have,
Perimeter = 2(2x + x)
Simplifying the expression, we get:
Perimeter = 2(3x)
Now, we are also given that the perimeter of the garden is 54 m. Substituting this value into the expression, we can solve for x:
54 = 2(3x)
Dividing both sides by 2:
27 = 3x
Dividing both sides by 3:
x = 9
So, the width of the garden is 9 meters.
To find the length, we can substitute the value of x back into our initial assumption:
Length = 2x
Length = 2(9)
Length = 18
Therefore, the length of the garden is 18 meters.
Finally, to find the perimeter, we use the formula 2(Length + Width):
Perimeter = 2(18 + 9)
Perimeter = 2(27)
Perimeter = 54
Hence, the perimeter of the rectangular garden is 54 meters.