Solution:Concept- Using the sine rule
, when a , b and c are the length of sides of the triangle and A, B,and C are the angles opposite to that sides a,b and c respectively .assume the length of one the sides of pentagon as x. we will use the sine rule to determine the value of x and we will multiply this value with 5 to find the perimeter.
All sides of the regular pentagon are equal. Assuming each side as x. name the pentagon MNOPQ. Now join the vertices N and Q to form a triangle . MNQ . also there , a rectangle BNQC formed.
since they are the opposite sides of rectangle BNQC
In triangle MNQ
Angle NMQ=108°, all internal angles of a regular pentagon is 108°.
Apply sine rule in triangle in MNQ
Using the conclusion,
Substituting , Cos 36
Perimeter of the pentagon =5x because all 5 sides are equal.
Hence, option (3) is the correct answer.