The perimeter of an equilateral triangle is 18. Find the measure of the altitude?

Firstly, altitude is a line which passes through a vertex of a triangle, and is at right angles to the opposite side.  General Info:  We know that each side of the triangle will be 6 (18/3 = 6). In this case, a is the first leg, b is the second leg and c is the hypothenuse. Pythagoras: C² = a² + b²  How do we work out this problem?   The altitude = a (variable) b (second leg) = 6/2 = 3 c (hypothenuse) = 6  c² = a² + b² (make a the subject of the formula) c² - b² = a² + b² - b² (subtract b from both sides) a² = c² - b² (simplify)  a² = 6²- 3² (plug in the values) a²  = 36 - 9 = 27 (simplify)  √a² = √27 (eliminate the exponent) a = 5.196152423  FINAL ANSWER: The altitude of this triangle will be 5.196152423