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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

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 quesno16 class=

Respuesta :

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,


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