The side of a square tile is \(x-8\) cm, and its area is 900 square cm. What is the value of \(x\)?
Answer and explanation
Correct answer: 38
The area of a square is (side)², so \((x-8)^2=900\). Thus, \(x-8=\pm 30\), but a side length must be positive; hence \(x-8=30\) and \(x=38\). Option A incorrectly treats 30, the side length, as the value of \(x\). Exam tip: reject a negative root when the expression represents a length.
Frequently asked questions
What is the correct answer to this question?
38
Why is this the correct answer?
The area of a square is (side)², so \((x-8)^2=900\). Thus, \(x-8=\pm 30\), but a side length must be positive; hence \(x-8=30\) and \(x=38\). Option A incorrectly treats 30, the side length, as the value of \(x\). Exam tip: reject a negative root when the expression represents a length.
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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