The perimeter of a triangle is 45 cm. For side and 9 cm are in the second side. The third side is twice the length of the first side. Find the length of side

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Step-by-step explanation:

31

Step-by-step explanation:

1) Let the first side of the triangle be "x"

2) Based on the word problem, the second side is "twice the length of the first" - that means multiply by 2 - so the second side can be represented by "2x"

3) Based on the word problem, the third side is "is 3 more than the first" - that means the addition of 3 - so the third side can be represented by "x+3".

4) Based on the word problem, the total perimeter is "31"

5) Now we can make an algebraic formula to figure out the length of each side:  Here we go!

            First Side              Second Side           Third Side           Perimeter

                 x           +           2x               +      (x + 3)        =        31

      ... first add together all of the "x"s

                               3x                           +      (x + 3)        =        31

                                                              4x        + 3          =       31

     ... now, let us remove "3" from both sides; since it is "+3" we will subtract "3" from each side

                                                             4x        + 3  -  3    =       31  -  3

      ... which leaves us with:

                                                                                 4x    =       28

      ... now, because we have "4x", which is the same as saying "4 times x", we have divide both sides by "4" to remove it from the "x":

                                                                                 4x    =       28

                                                                                  4     =       4

      finally we are left with:

                                                                                 x      =       7

Now, we can take "7" and find the sides of our triangle:

1) First side - we said was "x", therefore it is:  7

2) Second side - we said was "2x", which would be 2(7), therefore it is:  14

3) Third side - we said was "x + 3", which would be 7 + 3, therefore it is: 10

Now, to check that we are correct, the three sides should add up to the parameter total we were given, which was "31".  Let's check:

                   7 + 14 + 10  =  31

                      21    + 10  = 31

                             31      = 31

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