# In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes

**Solution:**

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. [Pythagoras theorem]

In ΔABC

AB = BC = CA

AD ⊥ BC ⇒ BD = CD = BC/2

Now In ΔADC

AC^{2} = AD^{2} + CD^{2}

BC^{2} = AD^{2} + (BC/2)^{2} [Since AC = BC and CD = BC/2]

BC^{2} = AD^{2} + BC^{2}/4

BC^{2} - BC^{2}/4 = AD^{2}

3BC^{2}/4 = AD^{2}

3BC^{2} = 4AD^{2}

**Video Solution:**

## In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.5 Question 16:

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes. Hence proved 3BC^{2} = 4AD^{2}