Question

The perimeter of a triangle is 57 centimeters. The longest side is 3 ​centimeter(s) less than the sum of the other two sides. Twice the shortest side is 15 centimeters less than the longest side. Find the lengths of each side of the triangle.

Answer 1

Let's say x is longest side, y is shortest side and z is the other side. So we have some equations such that

$x+y+z=57$ (by the first sentence)

$x=(y+z) -3$ (by the second sentence)

$2y=x-15$  (by the third sentence)

By the second equation, we have $y+z=x+3$ and if we use it in the first equation, then $x+y+z=x+(x+3)=57$. So $x=27$

Since $x=27$, if we use it in the third equation the we have $2y=x-15=27-15=12$ then $y=6$

Therefore $z=24$