The width of a rectangle is one half its length. The perimeter of the rectangle is 54 cm. What are the width and length of the rectangle?
Width = W.
Length = 2W.
2*W + 2*(2W) = 54
W = 9 cm = width.
Length = 2W = 18 cm.
w= 1/2(L)
perimeter rectangle = w + w + L + L = 2w + 2L
54 = 2w + 2L
54 = 2 (1/2)(L) + 2L
54 = 3L
L = 18 cm
w= 1/2 (L) = 1/2(18) = 9 cm
To solve this problem, we can set up an equation using the information given.
Let's assume that the width of the rectangle is represented by "w" and the length of the rectangle is represented by "l".
According to the problem, the width (w) is one half its length (l), which can be written as:
w = l/2
The formula for the perimeter of a rectangle is given by:
perimeter = 2(length + width)
In this case, the perimeter is given as 54 cm, so we can write the equation as:
54 = 2(l + w)
Substituting the value of w from the first equation into the second equation, we get:
54 = 2(l + l/2)
Simplifying the equation, we have:
54 = 2(3l/2)
Expanding the brackets, we get:
54 = 3l
Solving for l, we divide both sides of the equation by 3:
l = 54/3
l = 18
Now that we have the value of l, we can substitute it back into the first equation to find w:
w = l/2
w = 18/2
w = 9
Therefore, the width of the rectangle is 9 cm and the length of the rectangle is 18 cm.