A triangle is such that its medium side is three times as long as its shortest side, and its longest side is five inches longer than four times its shortest side. The perimeter of the triangle is 69inches. Find the length of the medium side of the triangle

Solution:

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: 

 

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

 

perimeter of the triangle is 69 inches means: 

 

Now we can substitute values: 

 

becomes 

 

Adding s-terms... 
 
 

so s=8 

Now