The length of a rectangle is 4.5 units longer than the width,w. Find the perimeter of the rectangle
Think about it. A rectangle has how many sides? Four? If the length is "x" and the width is "y", and we know what "x" is, and the width is 4.5 times that, we can determine what "y" is by doing what? In a rectangle, two sides are of equal length the other two sides are of equal length. So, we multiply the length by how many equal sides, and the width by how many equal sides? The perimeter is all four sides' dimensions added together. 2 * x plus 2 * y. Or add x twice and y twice, then add the two together. It will come out the same either way.
So, if the rectangle is one inch wide, it would be 4.5 inches long, right? It has two sides that are one inch, so that makes two inches. Two sides are 4.5 inches or a total of nine. The perimeter is the total of the distance of all four sides. What's the answer?
9+2w
To find the perimeter of a rectangle, we need to add up the lengths of all four sides.
Let's first define the width of the rectangle as "w". We are given that the length of the rectangle is 4.5 units longer than the width, so we can express the length as "w + 4.5".
The perimeter, P, is calculated by adding up all four sides of the rectangle:
P = 2 * (length + width)
Substituting the values we have:
P = 2 * (w + (w + 4.5))
P = 2 * (2w + 4.5)
P = 4w + 9
Therefore, the perimeter of the rectangle is 4w + 9 units.