The perimeter of a triangle is 31 the shortest side is 10 inches less than the longest side and the third side is 4 inches less than the longest side find the length of each side.

Shortest side = 5 units

Longest side = 15 units

Third side = 11 units

Step-by-step explanation:

To solve this, we write down each equation. I'll be using the variable a for the short side, b for the long side, and c for the third side:

a + b + c = 31 units

a = b - 10

c = b - 4

To solve for b, the long side, we can simply substitute a and c for their equivalent parts involving b into the original perimeter equation like so:

(b - 10) + b + (b - 4) = 31 units

Now we can solve for b by simplifying the equation above:

3b - 14 = 31 units

Simplify some more by adding 14 to both sides of the equation ...

3b = 45 units

And finally divide both sides by 3 to get:

b = 15 units

Now we can take the value of b and plug it into the equations involving a and c to solve for those:

a = 15 units - 10 units

Simplified:

a = 5 units

And

c = 15 units - 4 units

Simplified:

c = 11 units