When the side of a square field is increased by 4 m, its area increases by 96 m². What was the original side length?
Answer and explanation
Correct answer: 10 m
Let the original side be \(x\) m. The increase in area gives \((x+4)^2-x^2=96\). Expanding, \(x^2+8x+16-x^2=96\), so \(8x=80\) and \(x=10\) m. Therefore, option B is correct. Exam tip: if the side of a square increases by \(a\), the area increase is \(2ax+a^2\); here, \(2\times4\times x+4^2=96\) gives the answer directly.
Frequently asked questions
What is the correct answer to this question?
10 m
Why is this the correct answer?
Let the original side be \(x\) m. The increase in area gives \((x+4)^2-x^2=96\). Expanding, \(x^2+8x+16-x^2=96\), so \(8x=80\) and \(x=10\) m. Therefore, option B is correct. Exam tip: if the side of a square increases by \(a\), the area increase is \(2ax+a^2\); here, \(2\times4\times x+4^2=96\) gives the answer directly.
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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