Answer:
19 cm
Explanation:
Let's denote the three consecutive odd integers as x,x+2, and x+4 (since consecutive odd integers have a difference of 2).
The perimeter (P) of the triangle is the sum of the lengths of its three sides:
P =x+(x+2)+(x+4)
Given that P = 51 cm, we can set up an equation:
51 = 3x+6
Now, solve for
3x = 45
x = 15
Now that we have the value of x, we can find the lengths of the three sides:
Length of the first side (x): 15 cm
Length of the second side (x+2): 17 cm
Length of the third side (x+4): 19 cm
So, the length of the longest side is 19 cm