#1. a 30 inch wire is bent into a scalene triangle. its median side is 2 inches longer than
twice its shortest side, while its longest side is one inch longer than its median side
each of its side lengths?

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

Step-by-step 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