Let a , b , and c be the lengths of the sides of a triangle . If the circumradius of the triangle is 3, and a × b × c = 1 2 0 , then what is the area of this triangle ?
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Nice solution Jerry!
The area of a triangle can be written as 4 R a b c , where a b c is the product of the length of the sides of the triangle, and R is the circumradius of the triangle. Therefore, the area of this triangle is: 4 × 3 1 2 0 = 1 2 1 2 0 = 1 0
Very nice area identity! =D
Exactly what I did
a × b × c = 120 c / sin (A) = 2r = 6 ---> c = 6sin (A) Hence : a × b × 6sin (A) = 120 ---> a×b×sin (A) = 20 [a×b×sin (A)] / 2 = 10 ---> the area of a triangle
Sorry for not making it look fancy :P still learning.
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Using the sine rule, a = 6 sin A b = 6 sin B c = 6 sin C
The area of the triangle is given by Area = 2 1 a b sin C = 2 1 a b ⋅ 6 c = 1 2 1 a b c = 1 0