### Home > AC > Chapter 6 > Lesson 6.1.1 > Problem6-7

6-7.

Solve the problem below by defining a variable and then writing and solving an equation.

The perimeter of a triangle is $31$ cm. Sides $\#1$ and $\#2$ have equal length, while Side $\#3$ is one centimeter shorter than twice the length of Side $\#1$. How long is each side?

What must you guess and what must you check? Guess side 1 and check that the perimeter $=31$ What is the relationship between side 1 and the other sides?

$\text{Side #}1=\ \text{Side #}2$
$\text{Side #}3=2\left(\text{Side #}1\right)-1$
Make sure the sides sum to $31$.

$\text{Side #}1=\text{Side #}2\ \text{cm}$
What is the length of Side $\#3$?