A rectangular park is to be fenced along two breadths and one length, with a total fencing of 96 m. What should its breadth be for the area of the park to be maximum?
Answer and explanation
Correct answer: 24 m
Let the breadth be b m and the length be l m. From the three-sided fencing condition, l+2b=96, so l=96−2b. Hence, the area is A=b(96−2b)=−2b²+96b. This quadratic reaches its maximum at its vertex, where b=−96/(2×−2)=24 m. The corresponding length is 48 m and the maximum area is 1152 square m. Exam tip: For ax²+bx+c, the x-coordinate of the vertex is −b/(2a).
Frequently asked questions
What is the correct answer to this question?
24 m
Why is this the correct answer?
Let the breadth be b m and the length be l m. From the three-sided fencing condition, l+2b=96, so l=96−2b. Hence, the area is A=b(96−2b)=−2b²+96b. This quadratic reaches its maximum at its vertex, where b=−96/(2×−2)=24 m. The corresponding length is 48 m and the maximum area is 1152 square m. Exam tip: For ax²+bx+c, the x-coordinate of the vertex is −b/(2a).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
