Joe is designing a triangular garden in a corner of his backyard. The smallest side of the garden is

Question

Joe is designing a triangular garden in a corner of his backyard. The smallest side of the garden is one half12
of the length of the longest side. The middle side is 1 foot1 foot
shorter than the longest side. If he will need 1919
feet of fencing to surround the? garden, find the measure of the shortest side.

Answer 1

There are several typing errors in your problem statement which makes understanding the problem parameters a bit confusing, but the following is what I will be using in my explanation.  Let assign the following variables...

 

    x=longest side

 x-1=middle side, 1 foot shorter than

                   longest side, given

 x/2=shortest side, given

P(Δ)=1919ft total perimeter, given

 

So....

P(Δ)=long+middle+short...definition of

                                               perimeter

1919= x  + (x-1) + 0.5x.....substitute side length

                                            expressions

1919=2.5x-1.....combine like terms

1920=2.5x........add 1, both sides

 2.5x=1920.......rewrite

 ∴  x=768.........divide both sides by 2.5

 

So...

longest side...................x=768 feet

middle side = x-1=768-1=767 feet

shortest side=.......768/2=384 feet

 

Let's check our solution....

P(Δ)=long+middle+short...total perimeter

1919=768+767+384...........substitute calc'd

                                              side values

1919=1919..........................true, √check, our

                                              solution is correct

                                              for assumptions

                                              made

 

Always check your solution and work!

 

Note:

Should the wording or values of your original problem be different, make the appropriate changes to the variable side length assignments.  The calculation procedure remains the same.