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

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Answer 1 · 2016-04-28T19:21:05

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

Perimeter = 4

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 $h$

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

$x=12/3=4$

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Triangle has 3 sides and each side is 4

Perimeter is $3xx4=12$