Question

ABC is an equilateral triangle with side 2a, then the length of one of its altitude is_______

Answer 1

given -ABC is a equilateral triangle , side=2a

to find- length of one of its altitude

perpendicular² +base² =hypotenuse²

altitude² +(side/2)² = side²

altitude²+ a² = (2a)²

altitude² = 4a²- a²

altitude²= 3a²

altitude= √3  a    (ANS)

Answer 2

Answer:

the length of it's altitude = $\sqrt{3a^{2} }$ (or) $\sqrt{3} a$

Step-by-step explanation:

Apply pythagorus theorem on the attachment

$(2a)^{2} =a^{2} +x^{2}$

$4a^{2} -a^{2} =x^{2}$

$x=\sqrt{3a^{2} }$  (or)  $\sqrt{3} a$

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