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

$58, 60, 62$ $58, 60, 62$

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

$(n - 2), (n), (n + 2)$ $(n-2),(n),(n+2)$

are three consecutive even numbers.

Therefore

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

We can simplify so...

$3 n + 2 - 2 = 180$ $3n+2-2=180$

$3 n + 0 = 180$ $3n+0=180$

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

$\frac{3 n}{3} = \frac{180}{3}$ $(3n)/3=180/3$

$n = 60$ $n=60$

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

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

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

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