Perimeter of an equilateral triangle is 54 cm and length of the side of the triangle is 3 cm less than the radius of a circle. Find the difference between the circumference of the circle and perimeter of the triangleChoices:- 78cm 68cm 88cm 98cm
Question
Perimeter of an equilateral triangle is 54 cm and length of the side of the triangle is 3 cm less than the radius of a circle. Find the difference between the circumference of the circle and perimeter of the triangleChoices:- 78cm 68cm 88cm 98cm
Solution
Step 1: Find the length of the side of the equilateral triangle.
The perimeter of an equilateral triangle is given by 3a, where a is the length of a side. So, a = Perimeter/3 = 54/3 = 18 cm.
Step 2: Find the radius of the circle.
The problem states that the length of the side of the triangle is 3 cm less than the radius of the circle. So, the radius of the circle is 18 + 3 = 21 cm.
Step 3: Find the circumference of the circle.
The circumference of a circle is given by 2πr, where r is the radius. So, the circumference is 23.1421 = 131.88 cm (approximately).
Step 4: Find the difference between the circumference of the circle and the perimeter of the triangle.
The difference is 131.88 - 54 = 77.88 cm.
So, the closest answer is 78 cm.
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