A rectangle has perimeter . What is the largest possible area?
Answer and explanation
Correct answer: D.
- Step 1: Let the sides be and , since .
- Step 2: Area , a downward parabola with maximum at .
- Step 3: The maximum area is (a square).
Answer
.
Why not the others: The sides add to , so the area cannot exceed , which rules out and . A rectangle gives only .
Practise more Algebraic problem solving.
Free questions with an explanation for every one, and full timed TMUA mock tests.
More Algebraic problem solving questions
- Two numbers have sum and product . What is the sum of their reciprocals?
- The sum of the first number and twice the second is , and the product of the two is as large as possible for positive reals. What is the…
- What is the coefficient of in the expansion of ?
- For what value of does have a repeated root at a negative value of and ?