Answer: [tex]h = 11.26cm[/tex]
Step-by-step explanation:
Equilateral triangle has equal sides, let the side be [tex]xcm[/tex] , then the perimeter is [tex]3x[/tex]
Therefore:
[tex]3x = 39[/tex]
[tex]x = 39/3[/tex]
[tex]x = 13cm[/tex]
To find the altitude , we will apply Pythagoras theorem , that is
[tex]13^{2}=h^{2}+6.5^{2}[/tex]
Therefore:
[tex]h^{2}=13^{2}-6.5^{2}[/tex]
[tex]h^{2}=169-42.25[/tex]
[tex]h^{2}=126.75[/tex]
take the square root of both sides
[tex]h = 11.26cm[/tex]
