From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. If the lengths of the perpendiculars are a,b, and c, find the altitude of the triangle.
Answer:
a+b+c
- The following figure shows the required triangle:
- Let's assume the side of the equilateral triangle △ABC is x.
The area of the triangle △ABC 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 .