Answer:
the length of each side of the equilateral triangle = 17
Step-by-step explanation:
suppose the side length of equilateral triangle = x
The 3 side of right triangle formed (by side length): x-12 , x-13, x-14
(x-13)² + (x-14)² = (x-12)² .... Pythagorean theorem
x² -26x + 169 + x² -28x + 196 = x² -24x + 144
x² - 30x +221 = 0
(x- 17) (x - 13) = 0
x = 17 or x = 13
if x = 13 the right triangle will have a side length of 13-13=0 ... not solution
x = 17
check: 17-12=5 17-13=4 17-14=3
3²+4² = 25 = 5²
