A square tile has side \(x\) cm. When a 5 cm wide border is added around it, the total area of the outer square becomes 900 square cm. What is the original side of the tile?
Answer and explanation
Correct answer: 20 सेमी
The border adds 5 cm on each side, so the side of the outer square is \(x+5+5=x+10\) cm. Therefore, \((x+10)^2=900\), giving \(x+10=\pm 30\). Since a side length must be positive, \(x+10=30\), and hence \(x=20\) cm. The negative root is not physically valid. Exam tip: for a uniform border around a square, add twice the border width to the original side.
Frequently asked questions
What is the correct answer to this question?
20 सेमी
Why is this the correct answer?
The border adds 5 cm on each side, so the side of the outer square is \(x+5+5=x+10\) cm. Therefore, \((x+10)^2=900\), giving \(x+10=\pm 30\). Since a side length must be positive, \(x+10=30\), and hence \(x=20\) cm. The negative root is not physically valid. Exam tip: for a uniform border around a square, add twice the border width to the original side.
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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