if area of equilateral triangle is 9 root 3cm², then find the semi perimeter of the area
Answers
Answer:
Solution:- Since,it is an equilateral triangle,thus all sides of the triangle will be equal. Thus,the sides of the triangle are 6cm each. Thus,perimeter of the equilateral triangle is 18cm.
Step-by-step explanation:
Given:-
☆Area of an equilateral triangle:-
= > 9 \sqrt{3} {cm}^{2}=>9
3
cm
2
To find:-
☆Perimeter of the triangle
Solution:-
We know that area of an equilateral triangle is:-
= > \frac{ \sqrt{ 3} {a}^{2} }{4} sq.units=>
4
3
a
2
sq.units
Where 'a' is side of the triangle
= > \frac{ \sqrt{3} {a}^{2} }{4} = 9 \sqrt{3}=>
4
3
a
2
=9
3
= > {a}^{2} = \frac{4 \times 9 \sqrt{3} }{ \sqrt{3} }=>a
2
=
3
4×9
3
= > {a}^{2} = 36=>a
2
=36
= > a = \sqrt{36}=>a=
36
= > a = 6cm=>a=6cm
Since,it is an equilateral triangle,thus all sides of the triangle will be equal.
Thus,the sides of the triangle are 6cm each.
______________________________________
Now,perimeter of a triangle=sum of 3 sides
=>(6+6+6)cm
=>18cm
Thus,perimeter of the equilateral triangle is 18cm.
_______________________________________
Answer:
9cm
Step-by-step explanation:
......hope it helps you