Question

The lengths of the four sides of a quadrilateral (in meters) are consecutive even integers. If the perimeter is 5252 meters, find the value of the longest of the four side lengths.
Answer
Attempt 1 out of 2

Answer 1

Let the lengths of the four sides of the quadrilateral be represented as four consecutive even integers. We can denote them as:

- \( x \): the first even integer
- \( x + 2 \): the second even integer
- \( x + 4 \): the third even integer
- \( x + 6 \): the fourth even integer

The formula for the perimeter \( P \) of the quadrilateral is the sum of its side lengths:

\[
P = x + (x + 2) + (x + 4) + (x + 6)
\]

Combining the terms gives:

\[
P = 4x + 12
\]

We are told that the perimeter is 5252 meters, so we can set up the equation:

\[
4x + 12 = 5252
\]

To find \( x \), we first subtract 12 from both sides:

\[
4x = 5252 - 12
\]
\[
4x = 5240
\]

Next, divide both sides by 4:

\[
x = \frac{5240}{4} = 1310
\]

Now we can determine the lengths of all four sides:

- First side: \( x = 1310 \)
- Second side: \( x + 2 = 1312 \)
- Third side: \( x + 4 = 1314 \)
- Fourth side: \( x + 6 = 1316 \)

The longest of these four side lengths is:

\[
\text{Longest side} = x + 6 = 1316 \text{ meters}
\]

Therefore, the value of the longest of the four side lengths is \( \boxed{1316} \).