Question

in an equilateral triangle prove that three times the square of one side is equal to the four times the square of one of its altitudes ques.no.16

Answer 1

Answer:

See below.

Step-by-step explanation:

Let the side have a length x units .

The triangle formed by an altitude  is a 30-69-90 triangle so the sides are in the ratio 2:1:√3   where √3 is the altitude. Therefore if the side of the triangle = x then altitude = √3  * x / 2   =   √3x/2.

So we need to prove that  3x^2 =   4 (√3x/2)^2.

Simplifying:-

4 (√3x/2)^2 =  4 *( 3x^2/ 4) = 3x^2. This completes the proof,