SOLUTION: Please help... The perimeter of a triangle is 72cm. One side is four times the smallest side. The third side is 24cm longer than the smallest side. Find the measure of each side

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Please help... The perimeter of a triangle is 72cm. One side is four times the smallest side. The third side is 24cm longer than the smallest side. Find the measure of each side      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 217641: Please help...
The perimeter of a triangle is 72cm. One side is four times the smallest side. The third side is 24cm longer than the smallest side. Find the measure of each side.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=shortest side, y=second side, and z=third side

"The perimeter of a triangle is 72cm" means that x%2By%2Bz=72


"One side is four times the smallest side" means y=4x


and "The third side is 24cm longer than the smallest side" tells us that z=x%2B24


x%2By%2Bz=72 Start with the first equation.


x%2B4x%2Bx%2B24=72 Plug in y=4x and z=x%2B24


6x%2B24=72 Combine like terms on the left side.


6x=72-24 Subtract 24 from both sides.


6x=48 Combine like terms on the right side.


x=%2848%29%2F%286%29 Divide both sides by 6 to isolate x.


x=8 Reduce.


So the smallest side is 8 cm.


Now just plug in this value into the equations y=4x and z=x%2B24 to find 'y' and 'z'


y=4x=4%288%29=32


So one side is 32 cm long.


z=x%2B24=8%2B24=32


and the third side is 32 cm long (this is just a coincidence)

----------------------------------------------------------------------

Answer:

So the three sides are 8 cm, 32 cm, and 32 cm long.