A farmer makes a rectangular field with an area of 384 square metres. The length of the field is 8 metres more than its breadth. What is the breadth of the field?
Answer and explanation
Correct answer: 16 m
Let the breadth of the field be \(x\) metres. Then its length is \(x+8\) metres. Using the area, \(x(x+8)=384\), so \(x^2+8x-384=0\). Factoring gives \((x-16)(x+24)=0\), hence \(x=16\) or \(x=-24\). Since a length cannot be negative, the breadth is 16 m. Option B (24 m) is the corresponding length, not the breadth. Exam tip: Always reject negative roots when solving geometrical measurement problems.
Frequently asked questions
What is the correct answer to this question?
16 m
Why is this the correct answer?
Let the breadth of the field be \(x\) metres. Then its length is \(x+8\) metres. Using the area, \(x(x+8)=384\), so \(x^2+8x-384=0\). Factoring gives \((x-16)(x+24)=0\), hence \(x=16\) or \(x=-24\). Since a length cannot be negative, the breadth is 16 m. Option B (24 m) is the corresponding length, not the breadth. Exam tip: Always reject negative roots when solving geometrical measurement problems.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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