Question 860308: if the perimeter of an equilateral triangle is 54 cm what is the length of an altitude
Answer by 1335(25)   (Show Source):
You can put this solution on YOUR website! Calculate the length of one side. Since the triangle is equilateral, all three sides are the same length. Divde 54 by 3: 54/3=18. Now you know that each side is 18cm. (Hint: Draw a triangle for these next couple of steps.)Now draw a line from one vertex to a base. You should now have two right triangles. You also know that the line bisects (creates two equal parts) on the base. Since the base is 18cm, and the line bisects the base, each segment is 9cm. Now simply apply the pythagorean theorem (a^2+b^2=c^2): 9^2+b^2=18^2 = 81+b^2=324 = b^2=243 = b=square root of 243 = b=9 times the square root of 3. The altitude is 9 times the square root of 3 cm.
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