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The lengths of the four sides of a quadrilateral (in meters) are consecutive odd integers. If the perimeter is 104 meters, find the value of the longest of the four side lengths.
Answer: meters

The lengths of the four sides of a quadrilateral (in meters) are consecutive odd integers. If the perimeter is $104$ meters, find the value of the longest of the four side lengths. $\newline$ Answer: meters

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Evaluate two-variable equations: word problems

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

104

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

\newline

Answer: meters

Denote smallest odd integer: Let's denote the smallest odd integer length of the quadrilateral as $x$ . Since the sides are consecutive odd integers, the other three sides will be $x+2$ , $x+4$ , and $x+6$ respectively. $\newline$ The perimeter $P$ of the quadrilateral is the sum of its side lengths, so we have: $\newline$ $P = x + (x + 2) + (x + 4) + (x + 6)$ $\newline$ We know the perimeter $P$ is $104$ meters, so we can set up the equation: $\newline$ $104 = x + (x + 2) + (x + 4) + (x + 6)$
Calculate perimeter equation: Now, let's simplify and solve the equation for $x$ : $104 = 4x + 12$ Subtract $12$ from both sides to isolate the terms with $x$ : $104 - 12 = 4x$ $92 = 4x$ Now, divide both sides by $4$ to solve for $x$ : $92 \div 4 = x$ $23 = x$
Simplify and solve equation: Since $x$ represents the smallest odd integer length of the quadrilateral, the longest side will be $x + 6$ . We already found that $x = 23$ , so: $\newline$ Longest side = $x + 6$ $\newline$ Longest side = $23 + 6$ $\newline$ Longest side = $29$ meters

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