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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
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B
3 cm
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C
2 cm
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D
Cannot be determined.
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Solution

The correct option is C 2 cm
Let 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=360on=360o720n=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=5xx=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=3yy=63=2 cm


so, option (c) correct.

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