The length of a rectangle is 4 times the width. The perimeter is 50cm. Find the length and width. Write the equations. What is the length and width?
P = 2L + 2W
50 = 2W + 2(4W)
50 = 10W
50/10 = W
5 = W
To solve this problem, let's assign variables to the length and width of the rectangle. Let's say the width of the rectangle is 'w' cm. According to the problem, the length is four times the width, so the length of the rectangle would be '4w' cm.
The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
Plugging the given information into the formula, we have:
50cm = 2 * (4w + w)
Now, let's simplify the equation and solve for 'w'.
First, combine like terms inside the parentheses:
50cm = 2 * (5w)
Now, distribute the 2 to each term inside the parentheses:
50cm = 10w
Divide both sides of the equation by 10 to isolate 'w':
w = 5cm
So, the width of the rectangle is 5cm.
To find the length, substitute the value of 'w' back into the expression for the length:
Length = 4w = 4 * 5cm = 20cm
Therefore, the length of the rectangle is 20cm and the width is 5cm.