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The lengths of the four sides of a quadrilateral (in centimeters) are consecutive even integers. If the perimeter is 84 centimeters, find the value of the longest of the four side lengths.
Answer: centimeters

The lengths of the four sides of a quadrilateral (in centimeters) are consecutive even integers. If the perimeter is $84$ centimeters, find the value of the longest of the four side lengths. $\newline$ Answer: centimeters

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The lengths of the four sides of a quadrilateral (in centimeters) are consecutive even integers. If the perimeter is

84

centimeters, find the value of the longest of the four side lengths.

\newline

Answer: centimeters

Define Variable: Let's call the smallest side length $x$ . Then the other side lengths are $x+2$ , $x+4$ , and $x+6$ , since they are consecutive even integers.
Calculate Perimeter: The perimeter is the sum of all side lengths, so we have $x + (x+2) + (x+4) + (x+6) = 84$ .
Combine Like Terms: Combine like terms to get $4x + 12 = 84$ .
Solve for x: Subtract $12$ from both sides to get $4x = 72$ .
Find Longest Side: Divide both sides by $4$ to find $x$ , which gives us $x = 18$ .
Find Longest Side: Divide both sides by $4$ to find $x$ , which gives us $x = 18$ . The longest side is $x + 6$ , so we substitute $x$ with $18$ to get $18 + 6 = 24$ centimeters.

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