Answer: C) 5
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Work Shown:
s = square side length
A = area of square = 9x^2+12x+4
A = s^2
A = (ax+b)^2
A = a^2*x^2 + 2abx + b^2 .... apply the FOIL rule
A = 9x^2 + 12x + 4
Equating corresponding terms, we see that,
- a^2*x^2 = 9x^2 which shows that a^2 = 9 and that solves to a = 3, assuming 'a' is positive.
- 2abx = 12x leads to 2ab = 12 or ab = 6. Using a = 3 we can find that b = 2.
- b^2 = 4 solves to b = 2 which matches with the previous value of b found.
Using a = 3 and b = 2, the sum of the values is a+b = 3+2 = 5, so that's why the answer is choice C.
Side note: 9x^2 + 12x + 4 factors to (3x + 2)^2