A square field has a side length of \(x\) metres. If its side is increased by 12 metres, the area increases by 2448 square metres. What is the original side length \(x\)?
Answer and explanation
Correct answer: 96
The original area is \(x^2\), and the new area is \((x+12)^2\). Hence, \((x+12)^2-x^2=2448\), which gives \(24x+144=2448\). Therefore, \(24x=2304\) and \(x=96\) metres. Thus, 96 is correct. Exam tip: For such questions, use \((a+b)^2-a^2=2ab+b^2\) to simplify the calculation quickly.
Frequently asked questions
What is the correct answer to this question?
96
Why is this the correct answer?
The original area is \(x^2\), and the new area is \((x+12)^2\). Hence, \((x+12)^2-x^2=2448\), which gives \(24x+144=2448\). Therefore, \(24x=2304\) and \(x=96\) metres. Thus, 96 is correct. Exam tip: For such questions, use \((a+b)^2-a^2=2ab+b^2\) to simplify the calculation quickly.
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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