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.
