  ### Home > INT1 > Chapter 6 > Lesson 6.1.4 > Problem6-38

6-38.

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 #$1$. Determine how long each side is by completing parts (a) through (c) below.

1. Let $x$ represent the length of Side #$1$. What essential part of this let statement is missing? What is the length of Side #$2$? Side #$3$?

According to the problem, Side #$2$ is the same length as side #$1$.
Write an expression representing Side #$3$ using $x$

$\text{Side #}2 = x$
$\text{Side #}3 = 2x - 1$

2. Write a mathematical sentence that states that the sums of the sides equals the perimeter, which is $31$ cm.

$\text{Side #}1 +\text{ Side #}2 +\text{ Side #}3 = 31$

3. Solve the equation you found in part (b) and determine the length of each side. Be sure to label your answers with the appropriate units.

$x + x + 2x − 1 = 31$

Once you've found the value of $x$, find the length of the sides including the units.