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?

Question

Caroline Aucoin · Accepted Answer

#58, 60, 62#

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

#(n-2),(n),(n+2)#

are three consecutive even numbers.

Therefore

#(n-2)+(n)+(n+2) = "180 cm"#

We can simplify so...

#3n+2-2=180#

#3n+0=180#

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

#(3n)/3=180/3#

#n=60#

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

#(n-2)+(n)+(n+2)=180#

#(60-2)+(60)+(60+2)=180#

#58+60+62=180 -># check!

Carson Arnold · Answer

undefined Let $ x $ represent the length of the first side of the triangle. Since the sides are consecutive even integers, the second side would be $ x + 2 $ and the third side would be $ x + 4 $. According to the given information, the perimeter of the triangle is 180 centimeters.

Thus, we can write the equation:
$$ x + (x + 2) + (x + 4) = 180 $$

Solving this equation:
$$ 3x + 6 = 180 $$
$$ 3x = 180 - 6 $$
$$ 3x = 174 $$
$$ x = \frac{174}{3} $$
$$ x = 58 $$

So, the lengths of the three sides are 58, 60, and 62 centimeters.