Question

The perimeter of a regular pentagon is 100cm. How long is each side?

Answer 1

Hint: Use the fact that the sides of a regular pentagon are all equal and a pentagon has five sides. Assume that the side length of the pentagon is x. Hence find the perimeter in terms of x. Equate this expression to the perimeter of the pentagon, which is 100. Hence form an equation in x. Solve for x and hence find the length of the side of the pentagon.

Complete step-by-step answer:
Before solving the question, we need to understand what perimeter is and what is a regular pentagon.
The perimeter of a curve is the total length of its boundary. In other words, if the boundary of the curve is straightened, how long will the line segment so formed be the perimeter of the curve.
A pentagon is a polygon with five sides. A regular polygon is a polygon in which all angles and sides are equal. Hence a regular pentagon is a pentagon in which all the sides and angles are equal.
Consider the regular pentagon ABCDEA as shown below

Let the perimeter of the pentagon be 100 and let the length of side AB be x.
Since the pentagon is a regular pentagon, we have AB = BC = CD= DE = EA = x
Now, we know that the perimeter is the total length of the boundary of the curve.
Hence we have
Perimeter =AB + BC + CD + DE + EA = x+x+x+x+x = 5x
But, given the perimeter of the pentagon is 100.
Hence, we have 5x = 100
Dividing both sides by 5, we get
x = 20
Hence the length of the side of the pentagon is 20cm.

Note: Verification:
We have side length = 20
Hence the perimeter of the pentagon = 20+ 20 +20 +20 +20 = 100cm
Hence our answer is verified to be correct.