The Perimeter of a Rectangle
Given a rectangle of width w and length l, the perimeter is calculated as the sum of the side lengths, that is:
P = w + w + l + l
Or, equivalently
P = 2w + 2l
Hermann was calculating the perimeter of a rectangle and built the expression:
P = x + x + 4x + 4x feet
Note this expression is similar to the first one. This means that the width of the rectangle is x and the length is 4x.
a) We'll draw a rectangle with such dimensions:
b) Assuming the base is the length and the height is the width, the relationship between the base and the height is
4x / x = 4
This means the base is four times the height
c) We are given the perimeter as P = 60 feet.
We need to solve the equation
x + x + 4x + 4x = 60
Simplifying:
10x = 60
Dividing by 10:
x = 60/10
x = 6 feet
The base is 4x = 24 feet.
The base of Herman's rectangle is 24 feet
The height of Herman's rectangle is 6 feet