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?

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Answer 1 · 2018-04-23T09:05:12

#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!