From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. If the lengths of the perpendiculars are and , find the altitude of the triangle.
Answer:
- The following figure shows the required triangle:
- Let's assume the side of the equilateral triangle is .
The area of the triangle can be calculated using Heron's formula, since all sides of the triangles are known.
- Similarly, the area of the triangle
and the area of the triangle - By comparing the equations and we get:
- Now,
By putting the value of from the equation , we get,
Altitude of the triangle
Altitude of the triangle- Hence, the altitude of the triangle is .