The side of a square tile is \(x-12\) cm and its area is 1849 square cm. What is the value of \(x\)?
Answer and explanation
Correct answer: 55
The area of a square is the square of its side, so \((x-12)^2=1849=43^2\). Thus, \(x-12=43\) or \(x-12=-43\). Since a tile cannot have a negative side length, \(x-12=43\), giving \(x=55\). The negative algebraic root would make the side \(-43\) cm, which is not physically valid. In an exam, always apply the positive-length condition when taking a square root.
Frequently asked questions
What is the correct answer to this question?
55
Why is this the correct answer?
The area of a square is the square of its side, so \((x-12)^2=1849=43^2\). Thus, \(x-12=43\) or \(x-12=-43\). Since a tile cannot have a negative side length, \(x-12=43\), giving \(x=55\). The negative algebraic root would make the side \(-43\) cm, which is not physically valid. In an exam, always apply the positive-length condition when taking a square root.
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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