Question

If side of an equilateral triangle is x units what is its height

Answer 1

Step-by-step explanation:

draw a median to the triangle ABC. let the median be AD.

now ABD is. a right triangle where AB = x, BD = 1/2BC

BD = x/2

AD is the height

by Pythagoras theorem,

AD square + BD square = AB square

AD square = x square - x/2 square

= x square - xsquare / 4

= 4x square - x square /4

= 3 x square / 4

AD = √3x / 2 units

Answer 2

Step-by-step explanation:

Side of equilateral triangle = X units

Take equilateral triangle ABC

Draw a median D to BC

In triangle ABD:

AB^2 = AD^2 + BD^2

x^2 = AD^2 + (x/2)^2

x^2 = AD^2 + x^2/4

x^2 - x^2/4 = AD^2

4x^2/4 - x^2/4 = AD^2

3x^2/4 = AD^2

AD = root3x/ 2

Hope it helps you

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