# Altitude of a triangle?

• March 2nd 2009, 03:20 AM
captaintoast87
Altitude of a triangle?
The altitude of an equilateral triangle is 5 cm. Find the length of a side
• March 2nd 2009, 03:31 AM
Quote:

Originally Posted by captaintoast87
The altitude of an equilateral triangle is 5 cm. Find the length of a side

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

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

Thus

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

Hence

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

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