Answer
Each plot should have $12 \times 6.67$ or $10 \times 8$ as their dimensions.
Work Step by Step
Considering that the three garden plots will be placed horizontally like: $$\square \square \square$$ I am going to call the horizontal length of each garden plot by "a", and the height by "b".
As we can see, we have a total of 6 "a" segments, and 4 "b" segments. Thus their sum is equal to the total fencing material at hand, which is 88 ft.
$$6a + 4b = 88$$
And, we know that each plot is to be 80 $ft^2$, therefore:
$$a \times b = 80 $$ $$a = \frac{80} b$$
Substituting into the first equation:
$$6(\frac{80}b) + 4b = 88$$ $$\frac{480}{b} + 4b = 88$$ Multiplying both sides by "b": $$480+ 4b^2 = 88b$$ $$4b^2 - 88b + 480 = 0$$
Dividing both sides by "4":
$$b^2 - 22b + 120 = 0$$ $$b_1 = \frac{-(-22) + \sqrt{(-22)^2 - 4(1)(120)}}{2(1)}$$ $$b_1 = \frac{22 + \sqrt 4}{2} = \frac{24}{2} = 12$$ $$b_2 = \frac{22 - 2}{2} = 10$$
- Calculate $a_1$ and $a_2$:
$$a_1 = \frac{80}{b_1} = \frac{80}{12} = \frac {20}3 \approx 6.67$$ $$a_2 = \frac{80}{b_2} = \frac{80}{10} = 8$$
