Asked by Anonymous
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?
Answers
Answered by
Reiny
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
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
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