the width of a rectangle is one third of the length. of the perimeter is 40 cm find the dimension of the rectangle
Length = L
Width = L/3
P = 2L + 2L/3 = 40 cm. Solve for L.
To find the dimensions of the rectangle, we first need to set up a system of equations based on the given information.
Let's assume that the length of the rectangle is "x" cm.
Since the width of the rectangle is one-third of the length, the width would be (1/3) * x cm.
The formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, the perimeter is given as 40 cm, so we can write the equation as:
40 = 2(x + (1/3)x)
Let's solve this equation to find the value of "x", which represents the length of the rectangle:
40 = 2((4/3)x)
40 = (8/3)x
Next, we want to isolate "x" by multiplying both sides of the equation by (3/8):
(3/8) * 40 = (3/8) * (8/3)x
15 = x
Therefore, the length of the rectangle is 15 cm.
To find the width, we can substitute the value of the length into the equation for the width given above:
Width = (1/3) * 15
Width = 5 cm
So, the dimensions of the rectangle are 15 cm (length) and 5 cm (width).