Answer:
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.
