prove that height=√3/2 of equileateral triangle
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just use area of triangle formula
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you want to tell that height of a equilateral triangle is √ 3/2 of a side.
so let a triangle of side x.
In a triangle abc draw a perpendicular from vertex a to bc or from any vertex to it's corresponding side.
so,
ab ^2 = ad ^2 + (bc/2) ^2
x ^2 =ad ^2 + x ^2/4
ad ^2 = x ^2- x ^2/4
ad ^2= (4x ^2- x ^2)/4
ad ^2= 3x ^2/4
ad= √( 3x ^2/4)
ad = √ 3 x/2
so ad/ac = √ 3 x/2 × 1 /x.
= √ 3/2.
so let a triangle of side x.
In a triangle abc draw a perpendicular from vertex a to bc or from any vertex to it's corresponding side.
so,
ab ^2 = ad ^2 + (bc/2) ^2
x ^2 =ad ^2 + x ^2/4
ad ^2 = x ^2- x ^2/4
ad ^2= (4x ^2- x ^2)/4
ad ^2= 3x ^2/4
ad= √( 3x ^2/4)
ad = √ 3 x/2
so ad/ac = √ 3 x/2 × 1 /x.
= √ 3/2.
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