A square model shows parts \(x^2\), (12x), and (36). What side of the square does it indicate?
Answer and explanation
Correct answer: \(x+6\)
The total area is \(x^2+12x+36\). Here, \(36=6^2\) and the middle term is \(12x=2\cdot x\cdot 6\). Therefore, \(x^2+12x+36=(x+6)^2\), so the side of the square is \(x+6\). Squaring \(x-6\) would give a middle term of \(-12x\). Exam tip: for a perfect-square trinomial, check the square root of the constant term against the middle term.
Frequently asked questions
What is the correct answer to this question?
\(x+6\)
Why is this the correct answer?
The total area is \(x^2+12x+36\). Here, \(36=6^2\) and the middle term is \(12x=2\cdot x\cdot 6\). Therefore, \(x^2+12x+36=(x+6)^2\), so the side of the square is \(x+6\). Squaring \(x-6\) would give a middle term of \(-12x\). Exam tip: for a perfect-square trinomial, check the square root of the constant term against the middle term.
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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