Practical maximum and minimum problems: check 1
Difficulty: ★★☆Maths4U Original · Short practice
A rectangular growing area lies against a long wall. A total of 48 m of fencing covers the other three sides. The side parallel to the wall has length x and the perpendicular sides each have width y. Treat both dimensions as positive real numbers; ignore gate widths.
Write P=48 m for the total fencing length.
Find the width y giving the largest area.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Practical maximum and minimum problems: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
A rectangular growing area lies against a long wall. A total of 24 m of fencing covers the other three sides. The side parallel to the wall has length x and the perpendicular sides each have width y. Treat both dimensions as positive real numbers; ignore gate widths.
Write P=24 m for the total fencing length.
Find the width y giving the largest area.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Practical maximum and minimum problems: check 2
Difficulty: ★★☆Maths4U Original · Short practice
A rectangular growing area lies against a long wall. A total of 24 m of fencing covers the other three sides. The side parallel to the wall has length x and the perpendicular sides each have width y. Treat both dimensions as positive real numbers; ignore gate widths.
Write P=24 m for the total fencing length.
Find the fenced length x at the maximum-area configuration.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Practical maximum and minimum problems: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
A rectangular growing area lies against a long wall. A total of 28 m of fencing covers the other three sides. The side parallel to the wall has length x and the perpendicular sides each have width y. Treat both dimensions as positive real numbers; ignore gate widths.
Write P=28 m for the total fencing length.
Find the fenced length x at the maximum-area configuration.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Practical maximum and minimum problems: check 3
Difficulty: ★★☆Maths4U Original · Short practice
A rectangular growing area lies against a long wall. A total of 28 m of fencing covers the other three sides. The side parallel to the wall has length x and the perpendicular sides each have width y. Treat both dimensions as positive real numbers; ignore gate widths.
Write P=28 m for the total fencing length.
Find the maximum enclosed area.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Practical maximum and minimum problems: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
A rectangular growing area lies against a long wall. A total of 32 m of fencing covers the other three sides. The side parallel to the wall has length x and the perpendicular sides each have width y. Treat both dimensions as positive real numbers; ignore gate widths.
Write P=32 m for the total fencing length.
Find the maximum enclosed area.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Practical maximum and minimum problems: check 4
Difficulty: ★★☆Maths4U Original · Short practice
A rectangular growing area lies against a long wall. A total of 32 m of fencing covers the other three sides. The side parallel to the wall has length x and the perpendicular sides each have width y. Treat both dimensions as positive real numbers; ignore gate widths.
Write P=32 m for the total fencing length.
Find the area when y=P/5.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Practical maximum and minimum problems: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
A rectangular growing area lies against a long wall. A total of 36 m of fencing covers the other three sides. The side parallel to the wall has length x and the perpendicular sides each have width y. Treat both dimensions as positive real numbers; ignore gate widths.
Write P=36 m for the total fencing length.
Find the area when y=P/5.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.