Question

the lengths of the four sides of a quadrilateral (in meters) are consecutive integers. if the perimeter is 42 meters, find the value of the longest of the four side lengths.

Explanation:

Step1: Define variables for sides

Let the four consecutive integers representing the side lengths be \( n \), \( n + 1 \), \( n + 2 \), and \( n + 3 \), where \( n \) is the smallest side length.

Step2: Set up perimeter equation

The perimeter of a quadrilateral is the sum of its four side lengths. So, we have the equation:

$$ n+(n + 1)+(n + 2)+(n + 3)=42 $$

Step3: Simplify and solve for \( n \)

Combine like terms on the left - hand side:

$$ 4n+6 = 42 $$

Subtract 6 from both sides:

$$ 4n=42 - 6=36 $$

Divide both sides by 4:

$$ n=\frac{36}{4}=9 $$

Step4: Find the longest side

The longest side is \( n + 3 \). Substitute \( n = 9 \) into \( n + 3 \):

$$ n+3=9 + 3=12 $$

Answer:

The length of the longest side is 12 meters.