Answer:
7[tex]\sqrt{3}[/tex]
Step-by-step explanation:
the altitude creates two congruent 30-60-90° triangles
the ratio of the sides in a 30-60-90°, respectively, are 1 : [tex]\sqrt{3}[/tex] : 2
therefore we can set up a proportion to find the side length:
let 'x' = side length of equilateral Δ
[tex]\sqrt{3}[/tex] / 1 = 21 / x
cross-multiply:
[tex]\sqrt{3}[/tex]x = 21
x = 21 / [tex]\sqrt{3}[/tex]
rationalize the denominator by multiplying numerator and denominator by [tex]\sqrt{3}[/tex]
21[tex]\sqrt{3}[/tex] / [tex]\sqrt{3}[/tex]·[tex]\sqrt{3}[/tex] = 21[tex]\sqrt{3}[/tex] / 3 or 7[tex]\sqrt{3}[/tex]
