An altitude of an equilateral triangle is 30 inches. How do you find the perimeter of the triangle?

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Answer 1 · 2016-03-04T14:09:03

The perimeter #=60sqrt3# inches.

The formula for the altitude of an equilateral triangle is:
#color(blue)(sqrt3/2 xx # (side)

The altitude of the equilateral triangle is #30# inches.
Let the side of the triangle be denoted as #a#

#sqrt3/2 xxa = 30#

#a = 30 xx 2/ sqrt3#

#a = 60/ sqrt3#

Rationalising the denominator.

#a = (60 xx sqrt3)/ (sqrt3 xx sqrt3#

#a = (60 sqrt3)/ (3#

#a = 20 sqrt3#

The side, #a = 20 sqrt3# inches.

The perimeter of an equailateral triangle #= 3 xx a# (side)

# = 3 xx 20 sqrt3= 60sqrt3# inches.