Question

What is the perimeter of a regular pentagon with a side whose length is $$x+4$$ ?

Answer 1

Hint: Here in this question, we have to find the perimeter of a regular pentagon of given length $$l$$ using a formula $$P=5\times l$$ . If we are finding the perimeter of a regular pentagon, then we know that all five sides are equal lengths, so we can simplify the formula using multiplication operation to get the required solution.

Complete step-by-step answer:

In geometry, perimeter can be defined as the path or the boundary that surrounds a shape. It can also be defined as the length of the outline of a shape.
If a pentagon is regular, then all the sides are equal in length, and five angles are of equal measures
Consider a regular pentagon having length of $$x+4$$ , which is same for all sides of pentagon
The given regular pentagon has five equal sides. The perimeter is the distance around the outside of the pentagon. For a regular pentagon, the perimeter is the sum of the five sides or the length $$x+4$$ of a side multiplied by five.
 $$\Rightarrow P=5\times l$$
 $$\Rightarrow P=5\times \left(x+4\right)$$
On multiplication, we get
 $$\Rightarrow P=5x+20$$
Or the perimeter of regular pentagon can also find like
 $$\Rightarrow P=l+l+l+l+l$$
 $$\Rightarrow P=\left(x+4\right)+\left(x+4\right)+\left(x+4\right)+\left(x+4\right)+\left(x+4\right)$$
 $$\Rightarrow P=x+4+x+4+x+4+x+4+x+4$$
On simplification, we get
 $$\Rightarrow P=5x+20$$
Hence, the perimeter of a regular pentagon is $$5x+20$$ .
So, the correct answer is “ $$5x+20$$ ”.

Note: While determining the perimeter we use the formula. The unit for the perimeter will be the same as the unit of the length of a side or polygon. Whereas the unit for the area will be the square of the unit of the length of a polygon. We should not forget to write the unit with a final answer and we should also know about regular and irregular polygons.