Answer:
Fourth example, (2x - 3) and (x + 2), are possible dimensions
Step-by-step explanation:
Let's go through all the responses one by one;
First of all the area of the rectangular garden can be computed through length times width, such that:
(x^2 - 3) * (2) = 2x^2 + x - 6,
(2x + 3) * (x-2) = 2x^2 + x - 6,
(2x + 2) * (x-3) = 2x^2 + x - 6,
(2x - 3) * (x + 2) = 2x^2 + x - 6
Now in each of these examples, it should be that the products are equivalent to the area according to the length by width rule, so let's see which is truly the correct dimensions by justifying whether the product is truly equivalent to the area.
First example:
2 * (x^2 - 3) = 2x^2 - 6
Now 2x^2 - 6 ≠ 2x^2 + x - 6 so the first example is not a possibility,
Second example:
(2x + 3) * (x-2) = 2x^2- x - 6
Now 2x^2- x - 6 ≠ 2x^2 + x - 6 so the second example is not a possibility,
Third example:
(2x + 2) * (x-3) = 2x^2 - 4x - 6
Now 2x^2 - 4x - 6 ≠ 2x^2 + x - 6 so the third example is not a possibility,
Fourth example:
(2x - 3) * (x + 2) = 2x^2 + x - 6
Here 2x^2 + x - 6 = 2x^2 + x - 6 so the fourth example can act as possible dimensions
