SOLUTION: Help me this ones wrecking my brain and is stressing me out!!! The perimeter of a triangle ABC is 26m. BC is two thirds the length of AB and is 2m longer than ac. find the length

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Question 106679: Help me this ones wrecking my brain and is stressing me out!!!
The perimeter of a triangle ABC is 26m. BC is two thirds the length of AB and is 2m longer than ac. find the length of the sides.
Answer by rcmcc(152) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this question it is easier to make a set of simple equations.
because perimeter is x+y+z we can make the equation
ab%2Bbc%2Bac=26
now we can make equations for the other parts of the question
because BC is 2%2F3 the length of Ab we can make the equation
AB=%282%2F3%29BC
now we can add on the other part of the equation. because BC is 2cm longer than AC we can derive the equation
AC=BC%2B2
now you have the 3 equations below
ab%2Bbc%2Bac=26
AB=%282%2F3%29BC
AC=BC%2B2
the simplest way to solve is to substitute the 2 lower equations into the top equation in place of their respective variables. so you substitute (2/3)BC in place of AB in the top equation.
you get
%282%2F3%29BC%2BBC%2BBC%2B2=26
simplify
%288%2F3%29BC=24
divide by 8/3
BC=9
Now because you have BC solved substitute into the other equations to solve for the remainder sides
AC=9%2B2
AB=%282%2F3%299
so AC=11
and AB=6
the lengths of the 3 sides of the triagle are 9,11,6