The links of each side of a triangle is one of three consecutive numbers. If the perimeter is 48, what is the length of the longest side

The formula for perimeter of a triangle is P = a + b + c, where a, b, and c are the side lengths of the triangle. Since the sides of this triangle are consecutive numbers, they can be represented as follows.

a = a

b = a + 1

c = a + 2

The perimeter is known, so plug these values into the formula to find a.

P = a + b + c

48 = a + (a + 1) + (a + 2)

48 = a + a + 1 + a + 2

Collect like terms.

48 = 3a + 3

Subtract 3 from both sides.

45 = 3a

Divide both sides by 3.

15 = a

Calculate a + 1 and a + 2 by substitution to find the other two side lengths.

15 + 1 = 16

15 + 2 = 17

Answer:

The side lengths of the triangle are 15, 16, and 17.