tiangle pqr is an equilateral triangle in a circle. the height of the triangle is 18 cm. the diameter of the circle is 24 cm. find the perimeter of the triangle. can you help me solve this question?

1 answer

Quite easy ....

Make a sketch, draw in the altitude, and mark the centre.
The radius is 12 cm, and the distance from the centre to the triangle must then be 6 cm

You have a right-angled triangle with one leg 6, the hypotenuse as 12 and a missing base, call it x
x^2 + 6^2 =12^2
x^2 =108
x = √108 = 6√3
so each side of the triangle is 12√3
thus the perimeter is 36√3 cm