Question

if the length of a median of an equilateral triangle is 8 cm then find its area

Answer 1

Suppose,one side of triangle is y.

so, the base is also y . You all know median is bisect a line .

so one part of this side is y/2.

By pythogorus theorem,

Hypotonus^2 = Height^2 + Base^2

y^2 = 8^2 + (y/2)^2

8^2 = y^2 - y^2™/4

8^2 = 3y^2/4

y^2 = 4* 8^2 /3

y = 2*8/root3

So, one side is 16/root3

Area of equilateral triangle is = root3/4

Area = root3/4*16/root3*16/root3

= 64/root3 Ans