The lengths of the sides of a triangle are consecutive odd numbers. What is the length of the longest side if the perimeter is 45?

The longest side is 16.

Let the consecutive sides be y, y+1, and y+2.

The perimeter of a triangle is gotten by adding all its sides. Therefore, the perimeter will be:

y + y+1 + y+2 = 45

Collect like terms

3y = 45 - 3

3y = 42

Divide both side by 3

3y/3 = 42/3

y = 14

Therefore, the longest side will be:

y + 2 = 14 + 2 = 16

The longest side is 16.

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17

Step-by-step explanation:

Let x be the first side

x+2 is the next side ( consecutive odd number)

x+4 is the third side ( consecutive odd number)

P = x + x+2 + x+4

45 = x + x+2 + x+4

Combine like terms

45 = 3x+6

Subtract 6 from each side

45-6 = 3x+6-6

39 = 3x

Divide by 3

39/3 = 3x/3

13 =x

The longest side is

x+4

13+4 = 17

The longest side is 17