Answer:
9 cm
Explanation:
Applying,
P = a+b+c................. Equation 1
Where P = Perimeter of the triangle, a, b,c are the three sides of the triangle respectively.
From the question,
Given: P = 31 cm, a = x cm, b = (x-1) cm, c = (x+2) cm
Substitute these values into equation 1, and solve for x
31 = x+(x-1)+(x+2)
31 = 3x+1
3x+1 = 31
3x = 31-1
3x = 30
divide both side by 3 to get x
3x/3 = 30/3
x = 10.
Therefore, the sides of the triangle are
a = x = 10 cm,
b = (x-1) = (10-1) = 9 cm
c = (x+2) = (10+2) cm = 12 cm
Hence the shortest side is 9 cm