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19 March, 07:30

The perimeter of a triangle is 69 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 5 cm less than the sum of the other two sides. Find the lengths of the sides.

A. 17 cm; 21 cm; 31 cm

B. 15 cm; 21 cm; 33 cm

C. 16 cm; 21 cm; 32 cm

D. 15 cm; 22 cm; 32 cm

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Answers (1)
  1. 19 March, 10:02
    0
    option C

    Step-by-step explanation:

    We will call:

    a = the shortest side

    b = the middle side

    c = the longest side

    perimeter = p = 69cm

    So we have:

    69 = a+b+c equation 1

    a = b-5 equation 2

    c = a+b-5 equation 3

    Using equation 1 we have:

    69-c = a+b

    Using equation 3 we have:

    c+5=a+b

    we substitute equation 1 in equation 3:

    c+5=69-c

    2c=64

    c=64/2 so we have c = 32cm

    Using: c+5=a+b

    32+5=a+b

    37=a+b

    a=37-b

    Using equation 2 we have:

    37-b=b-5

    37+5=2b

    42/2=b we have b=21cm

    a=37-b=37-21 = 16 cm

    Finally: a=16 cm b=21 cm c=32cm
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