The length of a rectangle is twice the width. The perimeter is 42cm. find the length of each side.
l=2W
P=2L+2W=2(2W)+2W
solve for W, and then solve for L
2(2x)+2x=42
6x=42
x=7
width=7
length=14
To solve this problem, we can use the information given about the relationship between the length and width, as well as the formula for the perimeter of a rectangle.
Let's denote the width of the rectangle as "w" and the length of the rectangle as "l". The problem states that the length is twice the width, so we can write an equation for this relationship:
l = 2w (Equation 1)
The formula for the perimeter of a rectangle is:
perimeter = 2(length + width)
In this problem, the perimeter is given as 42cm, so we can write the equation:
42 = 2(l + w) (Equation 2)
Now we can substitute Equation 1 into Equation 2 to solve for the variables:
42 = 2(2w + w)
Simplifying:
42 = 2(3w)
Dividing both sides by 2:
21 = 3w
Finally, dividing both sides by 3, we find:
w = 7
Now, we can substitute the value of w back into Equation 1 to find the length:
l = 2w
l = 2(7)
l = 14
Therefore, the width of the rectangle is 7cm and the length is 14cm.