Question

The lengths of three perpendiculars from a point inside an equilateral triangle on the three sides are 16 cm, 25 cm and 28 cm. The area of the triangle (in cm2) will be

Answer 1

Answer:

2748 .76 cm²

Step-by-step explanation:

In any equilateral triangle, the sum of the perpendicular distances from any interior point to the sides of the triangle is equal to the altitude of the triangle

altitude of the triangle = 16 + 25 + 28 = 69 cm

Altitude of a triangle = a√3/2

a√3/2  = 69

=> a = 138/√3

Area of triangle = (√3/4)a²

= (√3/4) ( 138 / √3)²

= 69²/√3

= 2748 .76 cm²