Find the length.

Question

The perimeter of a triangle is 30in. The longest side is 2 less than 3 times the shortest side and the other side is 2 more than twice the shortest side. Find the length of each side.

Answer 1

The perimeter of a triangle is:  A + B + C, where A, B, and C are the side lengths.  The triangle in this problem has:

     A + B + C = 30 in       (eq1)

 

Then, the problem gives information about the relationship of the lengths of the sides (we can arbitrarily say that A is the shortest:

    C = -2 + 3A

    B = 2 + 2A

 

Substituting these values into eq1, we get an equation with only A (which we can solve):

    A   +  (2 + 2A)  +   (-2 + 3A)  = 30

     6A = 30                     [collect terms]

      A = 5

 

Now, put that value into the other two equations:

    C = -2 + 3A

    C = -2 + 15

    C = 13

 

 and

    B = 2 + 2A

    B = 2 + 10

    B = 12

 

Checking (very important):

  Is A + B + C = 30   ?

      5 + 12 + 13  = 30   ?

         30 = 30   ? yes

  Is  13 = -2 + 3*5   ?

       13 = -2 + 15   ?

       13  =  13   ? yes

  Is  12 = 2 + 2*5   ?

       12  = 12   ? yes