prove that height=√3\2a of equilateral triangle
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Answered by
10
Height of e triangle, let sides be a
Taking pythogoras theorem we can prove it
Taking pythogoras theorem we can prove it
Abhiranjanraj:
plz solve
Answered by
45
Heya..
Since Area of an equilateral triangle = √3 / 4 * side^2
=) 1/2 * base * height = √3 / 4 * side^2
Let side be a.
=) 1/2 * a * h = √3 / 4 * a^2.
=) h = 2√3 / 4 * a^2 /a
=) h = √3 / 2 * a
Or
Draw a equilateral triangle of side a.
Construct a height h.
Since altitude of equilateral triangle is equal to its median.
Hence height bisect the base.
By Pythagoras theorem,
=) h^2 + (a/2)^2 = a^2
=) h^2 + a^2 / 4 = a^2
=) h^2 = a^2 - a^2 /4
=) h^2 = 3a^2 /4
=) h = √3 / 2* a
Hope it's helpful to u.
Since Area of an equilateral triangle = √3 / 4 * side^2
=) 1/2 * base * height = √3 / 4 * side^2
Let side be a.
=) 1/2 * a * h = √3 / 4 * a^2.
=) h = 2√3 / 4 * a^2 /a
=) h = √3 / 2 * a
Or
Draw a equilateral triangle of side a.
Construct a height h.
Since altitude of equilateral triangle is equal to its median.
Hence height bisect the base.
By Pythagoras theorem,
=) h^2 + (a/2)^2 = a^2
=) h^2 + a^2 / 4 = a^2
=) h^2 = a^2 - a^2 /4
=) h^2 = 3a^2 /4
=) h = √3 / 2* a
Hope it's helpful to u.
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