(please explain with brief explanation)

Question

The sides of an equilateral triangle are shortened by 12 units,13 units and 14 units respectively and a right angled triangle is formed.Find the side of the equilateral triangle.

Answer 1

The side shortened least is longest, so
(x-14)^2 + (x-13)^2 = (x-12)^2

Now, we all know that the 3-4-5 triangle is the only one with sides which are consecutive integers. So, x-14=3, making x=17.

Solving the equation gives the same result.