What is the perimeter of an equilateral triangle whose height is 2(radical 3)?

1 Answer
Apr 28, 2016

Answer:

Socratic Formatting for radical is : hashsymbol sqrt(3) hashsymbol giving: #sqrt(3)#. Look at https://socratic.org/help/symbols.

Perimeter = 4

Explanation:

Let each triangle side be of length #x#

Let height be #h#

Then, by using Pythagoras

#h^2+(x/2)^2=x^2#

subtract #(x/2)^2# from both sides

#h^2=x^2-(x/2)^2#

#h^2=(4x^2)/4-x^2/4#

#h^2=3/4x^2#

Multiply both sides by #4/3#

#4/3 h^2=x^2#

Square root both sides

#x=(2h)/sqrt(3)#

Mathematicians do not like the denominator to be a radical

Multiply the right by 1 but in the form of #1=sqrt(3)/(sqrt(3)#

#x=(2hsqrt(3))/3#

But #h=2sqrt(3)# so by substitution for #h#

#x=(2(2sqrt(3))sqrt(3))/3#

#x=12/3=4#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Triangle has 3 sides and each side is 4

Perimeter is #3xx4=12#