The perimeter of a triangle is 51 cm the longest side is twice the length of the shorty start the third side is 3 cm longer than the shorter side where is the length of each side

The lengths of the sides are 15 cm , 17 cm and 19 cm.

Step-by-step explanation:

Step 1. Perimeter P means adding up all three sides.

Step 2. Let n be an odd integer.

Step 3. Let n+2 and n+4 be the next two consecutive odd integers.

Step 4. Then P=n+n+2+n+4=51.

Step 5. Solving the equation Step 4 yields the following steps

3n%2B6=51

Subtract 6 from both sides of the equation

3n%2B6-6=51-6

3n=45

Divide 45 to both sides of the equation

3n%2F3=45%2F3

n=15 Then n%2B2=17 and n%2B4=19. Also, P=15+17+19=51 which is a true statement.

Step 6. ANSWER: The lengths of the sides are 15 cm , 17 cm and 19 cm.