Final answer:
To find the smaller of two consecutive positive even numbers that multiply to 224, set up an equation and solve for the smaller number. The smaller number in this case is 14.
Step-by-step explanation:
To find the smaller of two consecutive positive even numbers, we need to determine the two numbers that multiply to give 224. Let's assume the smaller number is x. The next consecutive even number will be (x + 2). We can set up an equation: x(x + 2) = 224. Expanding and simplifying the equation, we get x^2 + 2x - 224 = 0. Factoring the quadratic equation gives us (x - 14)(x + 16) = 0. Solving for x, we find x = 14. Therefore, the smaller number is 14.
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