Question

The side of a rectangular pentagon is denoted by $ l $ . Express the perimeter of the pentagon using the variable $ l $ . \[\]

Answer 1

Hint: We recall the shape of a polygon and perimeter of a polygon. We recall the shape of a regular pentagon which has all its 5 sides of equal length and find its perimeter as the sum of the lengths of its 5 sides as an expression with the variable $ l $ .\[\]

Complete step by step answer:
We know from geometry that a polygon closed and a simple curve is made up of joining distinct points by line segments. Those points are called vertices and those line segments are called sides. If the length of all sides is equal, then we call the polygon regular polygon.\[\]
We also know that the perimeter of a geometrical shape in a plane is the measure of its outline. The perimeter of a polygon is the sum of lengths of its sides. \[\]
We know that the pentagon is a polygon with 5 sides and a regular pentagon will have lengths of its entire equal. We draw the pentagon ABCDE with sides AB, BC, CD, DE, and EA below. \[\]

We are given that length of one side is given to us in the question as $ l $ . Since all of the sides are of equal length we have
\[AB=BC=CD=DE=EA=l\]
 Let us denote the perimeter of the pentagon as $ P $ . Since perimeter is sum of lengths of sides we have;
\[\begin{align}
  & P=AB+BC+CD+DE+EA \\
 & \Rightarrow P=AB+BC+CD+DE+EA \\
 & \Rightarrow P=l+l+l+l+l \\
 & \therefore P=5l \\
\end{align}\]
The above expression is required an algebraic expression where $ l $ is the variable since if we take values of $ l $ we shall get different perimeters. \[\]

Note:
We note that an algebraic expression consists of variables and constants. We do not the values of variables and constants are numbers known to us. The obtained expression of the perimeter is linear since power on $ l $ is 1. We have shown the figure of the convex regular pentagon here. If we have the concave regular pentagon, the perimeter will not change.