The product of two consecutive positive even integers is equal to 360. What is the value of the greater integer?

The correct option is 20.

Step-by-step explanation:

Step 1: Define the variable.
Let $x$ represent the greater positive even integer.
Since consecutive even integers differ by 2, the smaller consecutive positive even integer will be $x-2$.

Step 2: Set up the product equation.
The problem states that the product of these two consecutive positive even integers is equal to 360. We can express this as an equation:

$x(x-2)=360$

Step 3: Form and solve the quadratic equation.
Expand the terms on the left side of the equation:

$x^2-2x=360$

Subtract 360 from both sides to rearrange the equation into standard quadratic form:

$x^2-2x-360=0$

Factor the quadratic expression by finding two numbers whose product is -360 and whose sum is -2. The two numbers are -20 and 18:

$(x-20)(x+18)=0$

Set each factor equal to zero to determine the possible values for $x$:

$x-20=0\Rightarrow x=20$

$x+18=0\Rightarrow x=-18$

Step 4: Select the valid positive solution.
Because the question asks for positive even integers, we discard $x=-18$ and retain $x=20$.

Step 5: Verify the answer.
If the greater integer is 20, the smaller integer is:

$20-2=18$

Checking their product:

$20\times 18=360$

This confirms that the value of the greater integer is indeed 20.