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30 August, 04:56

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

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  1. 30 August, 07:06
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    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.
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