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Question 28351: the altitude of an equilateral triangle is 12 centimeters. find the perimeter of the triangle.
thanks
Barbie
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! the altitude of an equilateral triangle is 12 centimeters. find the perimeter of the triangle.
In an equilateral triangle all the three sides are equal
say each side = (2x) units.
In an equilateral triangle, each altitude will also be median. That is the straight line drawn perpendicular from one vertex will meet the opposite side at its mid point.
Please draw the rough triangle as directed.
A triangle with sides looking equal each marked (2x) cms length.
Say the triangle is ABC.
Let M be the mid point of BC
Join A to M. Then AM is the altitude= 12cms
Since M is the mid point of Bc and BC = 2x cms this implies BM = CM = x cms
In the right angled triangle ABM, we have hypotenuse AB = (2x) cms, BM = x cms and AM = 12 cms.
Applying Pythog. Theorem, we have
AB^2 = BM^2 + AM^2
(2x)^2 = x^2 + 12^2
4x^2 = x^2+144
(4x^2-x^2) = 144
3x^2 = 144
x^2 = 144/3 = 3X48/3 = 48
x^2 = 48
gives x = sqrt(48) = sqrt(16X3) = 4 times sqrt(3)
Therefore each side = 2x cms = 2X(4 times sqrt(3) = 8(sqrt(3))
Perimeter of the equilateral triangle 3times (the length)
=3X[8(sqrt(3))]
=24times sqrt(3) cms
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