Answer:
The perimeter of triangle ABC is 15 cm
Step-by-step explanation:
we know that
An equilateral triangle has three equal sides and and three equal interior angles (each angle measure 60 degrees)
In this problem
Triangle ABC is an equilateral triangle
Because
AB=BC=AC
The area of a equilateral triangle (applying the law of sines) is equal to
[tex]A=\frac{1}{2}b^{2}sin(60^o)[/tex]
where
b is the length side of the equilateral triangle
we have that
[tex]A=\frac{25\sqrt{3}}{4}\ cm^2[/tex]
[tex]sin(60^o)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]\frac{25\sqrt{3}}{4}=\frac{1}{2}b^{2}(\frac{\sqrt{3}}{2})[/tex]
[tex]\frac{25\sqrt{3}}{4}=b^{2}(\frac{\sqrt{3}}{4})[/tex]
simplify
[tex]b^{2}=25[/tex]
[tex]b=5\ cm[/tex]
Find the perimeter of triangle ABC
The perimeter is equal to
[tex]P=3b[/tex]
substitute the value of b
[tex]P=3(5)=15\ cm[/tex]
