Answer:
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
