Question

what is the ratio of side and height of an equilateral triangle

Answer 1

Solution:

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Given & To Find :

The ratio of Height of equilateral triangle with it's side.

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We know that,

All the angles in an equilateral triangle is equal to 60°,.

This ratio can be calculated by,

Dividing the triangle into 2 equal parts,.

                A
                /l\
              /  l  \
        a  /    l   \ a
       B  /----l---\  C
           a/2 D a/2
           l--- a ---l

Here,  AD is the height of equilateral triangle,.

So, by pythagoras Theorem,

We get,

=> AD² + BD² = AB²

=> $AD^2 +( \frac{a}{2} )^2 = a^2$

=> $AD^2 + \frac{a^2}{4} = a^2$

=> $AD^2 = a^2- \frac{a^2}{4}$

=> $AD^2 = \frac{4a^2 - a^2}{4}$

=> $AD^2 = \frac{3a^2}{4}$

=> $AD = \sqrt{ \frac{3a^2}{4} }$

=> $AD = \frac{ \sqrt{3}a }{2} ..$


∴ Height of an equilateral triangle is $\frac{ \sqrt{3}a }{2}$

And hence, The ratio is,

=> $\frac{ \sqrt{3}a }{2} : a$

=> $\frac{ \sqrt{3} }{2} : 1$

=> $\sqrt{3} : 2$

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                                  Hope it Helps!!

Answer 2

Answer:

The ratio of the side of an equilateral triangle is 60

and its height is acute

Step-by-step explanation:

Hope this will help you

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