The perimeter of triangle ABC is 64 cm. Side AB is 7 cm less than side AC but 12 cm

The perimeter of triangle ABC is 64 cm. Side AB is 7 cm less than side AC but 12 cm larger than side BC. Find the length of each side of triangle ABC.

Perimeter of a triangle = the sum of all its sides. Let’s paint the perimeter.
AB + BC + AC = 64
AC-AB = 7 AC = 7 + AB
AB-BC = 12 BC = AB-12

AB + AB-12 + 7 + AB = 64
3AB-5 = 64
3AB = 69
AB = 23

Now we find the value of the other two sides of the triangle, thanks to the expressions AC = 7 + AB and BC = AB-12

AC = 7 + 23 = 30

BC = 23-12 = 11