A rectangle has a fixed perimeter of 28 cm. What is the largest possible area?
Answer and explanation
Correct answer: D. 49 cm^2
- Step 1: Let the sides be x and 14 - x. The area is A = x(14 - x).
- Step 2: A' = 14 - 2x = 0 gives x = 7, so the shape is a square with side 7 cm.
- Step 3: Maximum area = 7 x 7 = 49 cm^2.
Answer
49 cm^2.
Why not the others: '35 cm^2' uses sides that differ by 2, which is not the most square rectangle; '98 cm^2' doubles the correct area by using P^2/8 instead of P^2/16; '56 cm^2' adds one side to the maximum area.
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