Discussion
What is the longest side of a rectangle which has a perimeter of 70 units and an area of 276 square units?
Answer: C
The longest side is 23 units.
A perimeter of 70 means length + breadth = 35, and the area gives length × breadth = 276. So the sides are the roots of
\[ t^{2} - 35t + 276 = 0 \Rightarrow (t - 23)(t - 12) = 0 \]
The sides are 23 and 12, and 23 × 12 = 276 checks. 12 is the shorter side. 18 would need a breadth of 17, giving an area of 306, and 36 cannot be a side at all because the two sides add to only 35.
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