Question 1114865
The altitude cuts the equilateral triangle into two congruent special 30-60-90 right triangles, each with legs x and hypotenuse 2x:


The 2x would be ONE side of the equilateral triangle.


{{{15^2+x^2=4x^2}}}

{{{15^2=3x^2}}}

{{{3*5*15=3*x^2}}}

{{{5*15=x^2}}}

{{{x=sqrt(5*5*3)}}}

{{{x=5*sqrt(3)}}}

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Perimeter of equilateral triangle:
{{{3*2*5*sqrt(3)}}}

{{{30*sqrt(3)}}}