A square model shows \(4x^2+12x+9\). What will be its side?
Answer and explanation
Correct answer: \(2x+3\)
The given area \(4x^2+12x+9\) is a perfect-square trinomial: \(4x^2+12x+9=(2x)^2+2(2x)(3)+3^2=(2x+3)^2\). Hence, the side of the square is \(2x+3\). Squaring \(2x+6\) gives a middle term of \(24x\), not \(12x\). Exam tip: take the square roots of the first and last terms, then check whether the middle term equals \(2ab\).
Frequently asked questions
What is the correct answer to this question?
\(2x+3\)
Why is this the correct answer?
The given area \(4x^2+12x+9\) is a perfect-square trinomial: \(4x^2+12x+9=(2x)^2+2(2x)(3)+3^2=(2x+3)^2\). Hence, the side of the square is \(2x+3\). Squaring \(2x+6\) gives a middle term of \(24x\), not \(12x\). Exam tip: take the square roots of the first and last terms, then check whether the middle term equals \(2ab\).
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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