Question 743615
First we decide on names for our sides:

s-short side
m-medium
l-long

Next let's look at each statement carefully...


medium side is three times as long as its shortest side means:

{{{m=3s}}}

longest side is five inches longer than four times its shortest side means:

{{{l=4s+5}}}

perimeter of the triangle is 69 inches means:

{{{s+m+l=69}}}

Now we can substitute values:

{{{s+m+l=69}}}

becomes

{{{s+(3s)+(4s+5)=69}}}

Adding s-terms...

{{{8s+5=69}}}

{{{8s=64}}}

so s=8

Now 

{{{m=3s=3*8=24}}}