Question

Find the perimeter of a regular pentagon JENGU with the given consecutive vertices j(1,4) and e(3,1)

a-18.0 units
b-22.4 units
c-20 units 
d-25 units

Answer 1

We have been given two consecutive sides of a regular pentagon and we are asked to find out perimeter of pentagon. We are given the consecutive vertices j(1,4) and e(3,1).

In order to find perimeter of this pentagon we have to find out distance of two vertices using distance formula.

`D=\sqrt{(x_2-x_1)^(2)+(y_2-y_1)^(2)}`

Let
`x_2` be 1 and
`x_1` be 3. Similarly let
`y_2` be 4 and
`y_1` be 1.

Upon substituting our values in distance formula we will get,

`D=\sqrt{(1-3)^(2)+(4-1)^(2)}\\ =\sqrt{(-2)^(2)+(3)^(2)}\\ =√(4+9)\\ =√(13)=3.60555` units.

Now we will multiply our distance by 5 to get our perimeter as a regular pentagon has 5 equal sides.

Perimeter =
`3.60555\cdot 5=18.0277` units

Rounding our answer to nearest tenth we can see that option (a) is the right choice.