Asked by Baba Don Cooler
What equilateral triangle would have the same area as a triangle with side 6, 8 and 10?
Answers
Answered by
Reiny
did you notice that 6,8, and 10 forms a right-angled triangle (6^2 + 8^2 = 10^2)
so the area of the given triangle - (1/2)(6)(8) = 24
the area of an equilateral triangle with sides x is
(1/2)x^2 sin60° = √3/4 x^2
√3/4 x^2 = 24
x^2 = 96/√3
x = √(96/√3) = appr 7.44
so the area of the given triangle - (1/2)(6)(8) = 24
the area of an equilateral triangle with sides x is
(1/2)x^2 sin60° = √3/4 x^2
√3/4 x^2 = 24
x^2 = 96/√3
x = √(96/√3) = appr 7.44
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