$The area of a square is 9 x^{2} + 12 x + 4. What is the measure of the side of the square?$

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Solution

$This looks like the RHS of the algebraic identity: (a + b)^{2} = a^{2} + 2 a b + b^{2}$

$Comparing this with the given expression 9 x^{2} + 12 x + 4, we have a^{2} = 9 x^{2}, a = 3 x, b^{2} = 4, b = 2$

$9 x^{2} + 12 x + 4 = (3 x)^{2} + 2 (3 x) (2) + 2^{2}$

$= (3 x + 2)^{2}$

$Therefore, the side of the square is (3 x + 2) .$

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