Question

question
the lengths of the three sides of a triangle (in inches) are consecutive integers. if the perimeter is 27 inches, find the value of the shortest of the three side lengths.

Explanation:

Step1: Let the sides be x, x + 1, x + 2

Let the shortest side be $x$ inches. Then the other two sides are $x + 1$ inches and $x+2$ inches.

Step2: Set up perimeter equation

The perimeter of a triangle is the sum of its sides. So $x+(x + 1)+(x + 2)=27$.

Step3: Simplify the left - hand side

Combining like terms, we get $3x+3 = 27$.

Step4: Solve for x

Subtract 3 from both sides: $3x=27 - 3=24$. Then divide both sides by 3: $x=\frac{24}{3}=8$.

Answer:

8