Answer: the length of the longest side is 13 inches
the length of the of the median is 12 inches
the length of the of the smallest side is 5 inches
Explanation:
Let x represent the length of the of the longest side of the scalene triangle.
Let y represent the length of the of the median side of the scalene triangle.
Let z represent the length of the of the smallest side of the scalene triangle.
The formula for the perimeter of a triangle is the sum of the length of each side. If the 30 inch wire is bent into a scalene triangle, the perimeter would be 30 inches. it means that
x + y + z = 30 - - - - - - - - - - 1
Its median side is 2 inches longer than twice its shortest side. This means that
y = 2z + 2
2z = y - 2
z = y/2 - 1
Its longest side is one inch longer than its median side. This means that
x = y + 1
Substituting x = y + 1 and z = y/2 - 1 into equation 1, it becomes
y + 1 + y + y/2 - 1 = 30
Multiplying through by 2, it becomes
2y + 2 + 2y + y - 2 = 60
5y = 60
y = 12
Substituting y = 12 into x = y + 1,
x = 12 + 1 = 13
Substituting y = 12 into z = y/2 - 1, it becomes
z = 12/2 - 1 = 6 - 1 = 5