Question

Find the length of the side and perimeter of an equilateral triangle whose height is
13cm.​

Answer 1

Answer:

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Since,ABC is an equilateral triangle

CD is perpendicular bisector of AB

Now, according to Pythagoras theorem

in triangle ACD

AC²=AD²+CD²

(2a)²=(a)²+(13)²

4a²-a²=169

3a²=169

a²=169/3

a=√56

a=2√14cm

hence ,the length of the side of an equilateral triangle is 2√14cm

now , perimeter of the triangle =3(2√14)cm

=6√14cm