### Home > ACC7 > Chapter 9 Unit 10 > Lesson CC3: 9.2.1 > Problem9-59

9-59.

Write an equation to represent the situation below, and then answer the question.

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 $x$.
How do the other sides relate to the shortest side, or $x$?

Shortest Side: $x$
Medium side: $10 + 2x$
Longest Side: $3x$
Add the lengths of the sides and set equal to the perimeter in order to solve for $x$.

Shortest Side: $22$ cm
What are the lengths of the other sides?