To find the length of the longest side of a rectangular room given a perimeter of 70 meters, we can use the formula for the perimeter of a rectangle:
\[ P = 2(L + W) \]
where \(L\) is the length and \(W\) is the width of the room. Given that the perimeter \(P\) is 70 meters, we can set up the equation:
\[ 2(L + W) = 70 \]
Dividing both sides by 2, we get:
\[ L + W = 35 \]
To maximize the length \(L\), we can minimize the width \(W\). The smallest value \(W\) can take is greater than 0 (since width cannot be zero or negative). If we let \(W\) approach 0, then:
\[ L \approx 35 \]
Thus, the maximum possible length \(L\) approaches 35 meters. Therefore, the longest side of the room could be just under 35 meters, assuming a very small width.
In conclusion, the length of the longest side of the room could be approximately 35 meters.
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