The length of a rectangular garden is 2x and it's width is x-3. The garden's area is 80ft^2. Find the dimensions

The dimensions of the garden are 5 by 16 units

Step-by-step explanation:

The area of a rectangle is A = L * W. Here, (2x) * (x - 3) = 80 ft².

Let's multiply this result out and put it into standard quadratic form:

2x² - 6x - 80 = 0.

Dividing this entire equation through by 2 simplifies it to

x² - 3x - 40 = 0. Factors of 40 are 10 and 4, 8 and 5, and so on.

Note how 5 - 8 = - 3, which matches the coefficient of the x term. Thus, in factored form this quadratic is

(x - 8) (x + 3) = 0, so that x = 8 or x = - 3. Discard the negative root, since we're discussing real life measurements.

Then the dimensions of the garden are : L = 2x = 2 (8) = 16, and

W = x - 3 = 8 - 3 = 5.

Check: does 5 * 16 = 80? YES

The dimensions of the garden are 5 by 16 units.