The altitude of an equilateral triangle is 5 cm. Find the length of a side

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- Mar 2nd 2009, 02:20 AMcaptaintoast87Altitude of a triangle?
The altitude of an equilateral triangle is 5 cm. Find the length of a side

- Mar 2nd 2009, 02:31 AMADARSH
Let "a" be the side of an equilateral triangle.

altitude will fall on the midpoint of opp. side

Hence This makes a right triangle with**"a/2"**as__base__**"a"**as__hypotnuse__

and altitude as height

So using Pythagoras Theorem

$\displaystyle a^2 = a^2/4 + (altitude)^2 $

Thus

$\displaystyle 3a^2/4 = (Altitude)^2 $

Hence

$\displaystyle Altitude = \pm \sqrt{\frac{3a}{4}} $

-ve value for length is inappropriate So the answer is (Cake) tell me incase you can't digest this cake (Giggle)