A square field has a side length of \(x\) metres. If the side length is increased by 5 metres, the area increases by 425 square metres. What is the value of \(x\)?
Answer and explanation
Correct answer: 40
The original area is \(x^2\), while the new area is \((x+5)^2\). Thus, \((x+5)^2-x^2=425\), which simplifies to \(10x+25=425\). Hence, \(10x=400\) and \(x=40\) metres. Therefore, option C is correct. Exam tip: For such problems, equate the difference of the two areas before solving the resulting linear equation.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
The original area is \(x^2\), while the new area is \((x+5)^2\). Thus, \((x+5)^2-x^2=425\), which simplifies to \(10x+25=425\). Hence, \(10x=400\) and \(x=40\) metres. Therefore, option C is correct. Exam tip: For such problems, equate the difference of the two areas before solving the resulting linear equation.
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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