The altitude of an equilateral triangle is 18 inches. What is the length of a side?

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May 14, 2016

Answer:

The side # color(blue)( = 12sqrt3 # inches.

Explanation:

The altitude of the triangle #= color(blue)( 18# inches

Let us denote the side of the triangle as #a#.

The formula for calculating the altitude of an equilateral triangle is :

Altitude #= sqrt3/ 2 xx a # (side)

# 18 = sqrt3/ 2 xx a #

# a = 18 xx 2 / sqrt3 #

# a = 36/ sqrt3 #

# a = (36 xx color(blue)(sqrt3)) / (sqrt3 xx color(blue)(sqrt3) #

# a = (36 sqrt3) / 3 #

# a = 12sqrt3 # inches.

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May 14, 2016

Answer:

Length of the side of the triangle is #12sqrt3# inches.

Explanation:

If the length of the side of a triangle is #a# and #h# be its height as shown below.
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As the perpendicular from vertex divides base equally, we can find height #h# using Pythagoras theorem

Hence #h=sqrt(a^2-(a/2)^2)=sqrt(a^2-a^2/4)=sqrt(3a^2/4)=sqrt3/2a#

But as height is #18# inches, #sqrt3/2a=18# or

#a=18xx2/sqrt3=36sqrt3/3=12sqrt3#

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