The perimeter of a triangle is given by the sum of all it is sides.
Now, we have the next measures:
- The longest side of a triangle is 5in longer than the shortest side.
- The medium side is 4 inches longer than the shortest side
Then, the perimeter is given by:
P = (s+5)+(s+4)+s
If the perimeter is P=21 inches:
21 = (s+5)+(s+4)+s
Solve for s:
21 = s+5+s+4+s
21 = 3s + 9
21-9 = 3s
12 = 3s
s = 12/3
s= 4
Therefore,
The shortest side of the triangle is 4 inches.
The medium side is s+ 4 = 4+ 4 = 8 inches
The longest side is s+5 = 4+5 = 9 inches