SOLUTION: What is the ratio of the altitude to the side in an equilateral triangle? A ) 4 : 3 B ) 3 : 4 C ) 3 : 2 D ) 2 : 3

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Question 376207: What is the ratio of the altitude to the side in an equilateral triangle?
A ) 4 : 3 B ) 3 : 4 C ) 3 : 2 D ) 2 : 3

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If you add an altitude to an equilateral triangle, you have a right triangle with hypotenuse s, leg s%2F2, and leg of altitude h.
Use the Pythagorean theorem,
h%5E2%2B%28s%2F2%29%5E2=s%5E2
h%5E2%2Bs%5E2%2F4=s%5E2
h%5E2=%283%2F4%29s%5E2
h=%28sqrt%283%29%2F2%29s
So then the ratio of the altitude h to side s is
highlight%28h%2Fs=sqrt%283%29%2F2%29