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The side of a square tile is \((x-3)\) cm and its area is \(441\) cm². If the side length is positive, what is the value of \(x\)?
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Answer and explanation
Correct answer: 24
The area of a square is \((\text{side})^2\), so \((x-3)^2=441=21^2\). Thus, \(x-3=\pm21\). Since a side length must be positive, \(x-3=21\), giving \(x=24\). Exam tip: when taking the square root of an equation, consider both signs and then apply the length constraint.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
The area of a square is \((\text{side})^2\), so \((x-3)^2=441=21^2\). Thus, \(x-3=\pm21\). Since a side length must be positive, \(x-3=21\), giving \(x=24\). Exam tip: when taking the square root of an equation, consider both signs and then apply the length constraint.
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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