Answer :
The formula for determining the area of a triangle is expressed as
Area = 1/2 x base x height
The formula for determining the area of an equilateral triangle is expressed as
[tex]\text{Area = }\frac{a^2\sqrt[]{3}^{}}{4}[/tex]where a is the length of each side of the triange.
Given that the area of the triangle is 25√3, we have
[tex]\begin{gathered} 25\sqrt[]{3}\text{ =}\frac{a^2\sqrt[]{3}^{}}{4} \\ a^2\sqrt[]{3}\text{ = 4 x 25}\sqrt[]{3} \\ a^2\text{ = }\frac{100\sqrt[]{3}}{\sqrt[]{3}} \\ a^2\text{ = 100} \\ a\text{ = }\sqrt[]{100} \\ a\text{ = 10} \end{gathered}[/tex]The formula for determining the altitude is
[tex]\begin{gathered} h\text{ = }\frac{a\sqrt[]{3}}{2} \\ h\text{ = }\frac{10\sqrt[]{3}}{2} \\ h\text{ = 5}\sqrt[]{3} \end{gathered}[/tex]The length of each side is 10
The altitude is 5root3