SOLUTION: The sides of an equilateral triangle or shortened by 12 units, 13 units, and 14 units respectively and a right Angle triangle is formed. I need to find the length of each side of t

The Pythagoras says


      +  = ,


and it is what you should solve to find x, the side length of the equilateral triangle.



            Can you guess, how I determined that (x-14) and (x-13) are the legs ?

            - Because the hypotenuse is the longest side.



So, one way for you is to solve this quadratic equation.



            But it is a long and BORING WAY.

            There is another, more quick way.




Indeed, there is only one appropriate right angle triangle
for which one leg is one unit longer than the shortest leg
and the hypotenuse is one unit longer than the longest leg.


It is (3,4,5) - right angled triangle,

    so  x-12 = 5  and  x = 17.


ANSWER.  The side length of the equilateral triangle is 17 cm.


CHECK.  (17-13)^2 + (17-14)^2 = 4^2 + 3^2 = 16 + 9 = 25 = 5^2 = (17-12)^2.