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Write an equation to represent this situation and answer the question. Use the 5-D Process to help you define a variable and write an equation if necessary.

Ella is trying to determine the side lengths of a triangle. She knows that the longest side is three times longer than the shortest side. The medium side is ten more than twice the shortest side. If the perimeter is 142 cm, how long is each side?  

Create a variable expression for perimeter to represent this problem with the shortest side defined by . How do the other sides relate to the shortest side, or ?

Shortest Side:

Medium side:

Longest Side:

Sum the lengths of the sides and set the sum equal to the perimeter in order to solve for .

Shortest Side: cm
What are the lengths of the other sides?