Question

the lengths of the three sides of a triangle (in feet) are consecutive even integers. if the perimeter is 60 feet, find the value of the shortest of the three side lengths.

Explanation:

Step1: Let the sides

Let the shortest side length be $x$ feet. Since the sides are consecutive even integers, the other two sides are $x + 2$ feet and $x+4$ feet.

Step2: Set up perimeter equation

The perimeter of a triangle is the sum of its side - lengths. So, $x+(x + 2)+(x + 4)=60$.

Step3: Simplify the left - hand side

Combine like terms: $3x+6 = 60$.

Step4: Solve for $x$

Subtract 6 from both sides: $3x=60 - 6=54$. Then divide both sides by 3: $x=\frac{54}{3}=18$.

Answer:

18