Word Problem

Question

A triangular field is surrounded by 880 yards of fence.  The longest side of the field is 20 yards less than three times the length the shortest side. The length of the next-longest side is two times the length of the shortest side. What is the length of the shortest side?  

Answer 1

If you assign the shortest sign the variable 'x' then the longest side would be '3x-20' (three times the shortest side minus 20 yards) and the next longest side would be '2x' (two times the length of the shortest side).

 

The amount of fence needed to go all around the triangular field is the perimeter which is the sum of all the sides.

 

shortest side = x

next-longest side = 2x

longest side = 3x-20

 

perimeter = shortest side + next-longest side + longest side

 

880 = x + 2x + (3x-20)

880 = x + 2x + 3x -20

880 = 6x -20

880+20 = 6x-20+20

900 = 6x

900/6 = 6x/6

150 = x

 

so:

 

shortest side 'x' = 150 yards

next-longest side 2x = 2(150) = 300 yards

longest side '3x-20' = 3(150) - 20 = 430 yards