Question 217641
Let x=shortest side, y=second side, and z=third side


"The perimeter of a triangle is 72cm" means that {{{x+y+z=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+24}}}



{{{x+y+z=72}}} Start with the first equation.



{{{x+4x+x+24=72}}} Plug in {{{y=4x}}} and {{{z=x+24}}}



{{{6x+24=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=(48)/(6)}}} 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+24}}} to find 'y' and 'z'



{{{y=4x=4(8)=32}}}



So one side is 32 cm long.



{{{z=x+24=8+24=32}}}



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


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Answer:


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