the width of a rectangle is one half its lengh. The perimeter of the rectangle is 54 cm. What are the width and length of the Rectangle?
P = 2L + 2W
54 = 2L + 2(0.5L)
54 = 2L + L
54 = 3L
54/3 = L
18 = L
To solve this problem, we can start by setting up a system of equations using the given information.
Let's say the length of the rectangle is L cm. According to the problem, the width of the rectangle is half its length, so the width would be (1/2)L cm.
The perimeter of a rectangle is calculated by adding all four sides together. In this case, we can express the perimeter as:
Perimeter = 2(Length) + 2(Width)
Since the perimeter is given as 54 cm, we can substitute the expressions for length and width into the equation:
54 = 2L + 2(1/2)L
Simplifying this equation, we have:
54 = 2L + L
Combine like terms:
54 = 3L
Now, divide both sides of the equation by 3 to isolate L:
L = 54/3
L = 18
Therefore, the length of the rectangle is 18 cm.
To find the width, we can substitute the value of L into the expression for the width:
Width = (1/2)L = (1/2)(18) = 9
Thus, the width of the rectangle is 9 cm.
In summary, the length of the rectangle is 18 cm, and the width is 9 cm.