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If \(x^2+12x+36\) is a perfect square area model, what is the whole side?
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Answer and explanation
Correct answer: \(x+6\)
\(x^2+12x+36=x^2+2\cdot x\cdot6+6^2=(x+6)^2\). Thus, the square’s area is \((x+6)^2\), so its whole side is \(x+6\). If the side were \(x+12\), the middle term would be \(24x\), not \(12x\). Exam tip: use the identity \(x^2+2ax+a^2=(x+a)^2\).
Frequently asked questions
What is the correct answer to this question?
\(x+6\)
Why is this the correct answer?
\(x^2+12x+36=x^2+2\cdot x\cdot6+6^2=(x+6)^2\). Thus, the square’s area is \((x+6)^2\), so its whole side is \(x+6\). If the side were \(x+12\), the middle term would be \(24x\), not \(12x\). Exam tip: use the identity \(x^2+2ax+a^2=(x+a)^2\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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