A square field has a side length of \(x\) metres. If its side is increased by 10 metres, its area increases by 1700 square metres. What is the original side length \(x\)?
Answer and explanation
Correct answer: 80
The original area is \(x^2\), and the new area is \((x+10)^2\). Hence, \((x+10)^2-x^2=1700\), which gives \(20x+100=1700\). Therefore, \(20x=1600\) and \(x=80\) metres, so option B is correct. Exam tip: represent the increase as the difference of the two areas; it is not merely \(10^2\).
Frequently asked questions
What is the correct answer to this question?
80
Why is this the correct answer?
The original area is \(x^2\), and the new area is \((x+10)^2\). Hence, \((x+10)^2-x^2=1700\), which gives \(20x+100=1700\). Therefore, \(20x=1600\) and \(x=80\) metres, so option B is correct. Exam tip: represent the increase as the difference of the two areas; it is not merely \(10^2\).
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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