Question

the lengths of the four sides of a quadrilateral (in meters) are consecutive odd integers. if the perimeter is 40 meters, find the value of the longest of the four side lengths.

Explanation:

Step1: Let the first odd - integer side length

Let the first odd - integer side length be $x$. Then the other three consecutive odd - integer side lengths are $x + 2$, $x+4$, and $x + 6$.

Step2: Set up the perimeter equation

The perimeter of a quadrilateral is the sum of the lengths of its four sides. So, $x+(x + 2)+(x+4)+(x + 6)=40$.

Step3: Simplify the left - hand side of the equation

Combining like terms, we get $4x+12 = 40$.

Step4: Solve for $x$

Subtract 12 from both sides: $4x=40 - 12=28$. Then divide both sides by 4: $x=\frac{28}{4}=7$.

Step5: Find the longest side length

The longest side length is $x + 6$. Substitute $x = 7$ into $x + 6$, we get $7+6 = 13$.

Answer:

13