Question

area of an equilateral triangle is 25√3cm^2,then find altitude of triangle ​

Answer 1

Answer: $5\sqrt3$

Step-by-step explanation:

Given: The area is $25\sqrt{3}\,\rm{cm}^2$.

Calculate the length of the side of the triangle.

$\begin{aligned}\rm{Area}&=\frac{\sqrt3}{4}a^2 \\25\sqrt{3}&=\frac{\sqrt3}{4}a^2 \\a^2&=25\sqrt{3}\left(\frac{4}{\sqrt3}\right)\\a^2&=100\\a&=10\end{aligned}$

Calculate the length of the Altitude.

$\begin{aligned}\sin60^\circ&=\frac{\rm{altitude}}{a}\\\frac{\sqrt3}{2}&= \frac{\rm{altitude}}{10}\\\rm{altitude}&=\frac{\sqrt3}{2}\times 10\\&=5\sqrt3\end{aligned}$