The area of a square is \(225\text{ cm}^2\). When its side is increased by \(x\text{ cm}\), the new area becomes \(400\text{ cm}^2\). What is the value of \(x\)?
Answer and explanation
Correct answer: \(5\text{ cm}\)
The original side of the square is \(\sqrt{225}=15\text{ cm}\), and the new side is \(\sqrt{400}=20\text{ cm}\). Thus, \(15+x=20\), giving \(x=5\text{ cm}\). Option B is incorrect because a side of \(15+4=19\text{ cm}\) would produce an area of \(361\text{ cm}^2\), not \(400\text{ cm}^2\). Exam tip: take the square root of each area to find the corresponding side, then subtract the original side from the new side.
Frequently asked questions
What is the correct answer to this question?
\(5\text{ cm}\)
Why is this the correct answer?
The original side of the square is \(\sqrt{225}=15\text{ cm}\), and the new side is \(\sqrt{400}=20\text{ cm}\). Thus, \(15+x=20\), giving \(x=5\text{ cm}\). Option B is incorrect because a side of \(15+4=19\text{ cm}\) would produce an area of \(361\text{ cm}^2\), not \(400\text{ cm}^2\). Exam tip: take the square root of each area to find the corresponding side, then subtract the original side from the new side.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
