Question

#1. A 30 inch wire is bent into a scalene triangle. Its median side is 2 inches longer than

Answer 1

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

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