Question

# The perimeter of regular polygon having one of its exterior angle as 72o is 30 cm. What is the length of side of equilateral triangle whose perimeter is equal to the length of one side of the polygon?

A
6 cm
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
3 cm
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
2 cm
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Cannot be determined.
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is C 2 cmLet the number of sides of the polygon be n. Hence, number of exterior angles of the regular polygon will be also n. Given that one exterior angle is 72o Hence, sum of all exterior angles of the regular polygon will be n×72o because all exterior angles of a regular polygon are equal in measure. We know that sum of all exterior angles of a polygon is 360o So, n×72o=360o⇒n=360o720⇒n=5 Hence, the regular polygon is a regular pentagon Given: It has perimeter 30 cm. Because all sides of a regular polygon are equal, let length of each side of pentagon be x. Now, perimeter=5x 30=5x⇒x=305=6 cm Now, let the equilateral triangle have the side y. We know perimeter of triangle=3y Given: Perimeter of the equilateral triangle is equal to side length of the regular pentagon which is 6 cm. So, 6=3y⇒y=63=2 cm so, option (c) correct.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Sum of All Exterior Angles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program