# Three sides of a triangle are consecutive even integers and the perimeter of the triangle is 180 centimeters. What is the length of each of the three sides?

Apr 23, 2018

$58 , 60 , 62$

#### Explanation:

Three consecutive even numbers can be expressed in terms of $n$. If $n$ is an even number then

$\left(n - 2\right) , \left(n\right) , \left(n + 2\right)$

are three consecutive even numbers.

Therefore

$\left(n - 2\right) + \left(n\right) + \left(n + 2\right) = \text{180 cm}$

We can simplify so...

$3 n + 2 - 2 = 180$

$3 n + 0 = 180$

Divide both sides by $3$ to solve for $n$

$\frac{3 n}{3} = \frac{180}{3}$

$n = 60$

$60$ is an even integer. Input $60$ into the original equation.

$\left(n - 2\right) + \left(n\right) + \left(n + 2\right) = 180$

$\left(60 - 2\right) + \left(60\right) + \left(60 + 2\right) = 180$

$58 + 60 + 62 = 180 \to$ check!