I am helping my daughter with her high school pre-calc. We've both got stuck on this. Below is a copy of the exercise as presented.
We've come up with the following equations (none of which are in the answer set).
$$ A = -y^2 + 600y $$ $$ A = -x^2 + 300x $$
Since both areas are equal:
$$ -y^2 + 600y = -x^2 + 300x $$ or $$ y^2 - 600y = x^2 - 300x $$
Three trivial solutions (out of infinitely many): $(0,0),(300,0)$ and $(0,600)$ (curious ways to build a fence) can be seen in the graph below. Knowing the area would not make this problem seem any less strange.
Am I missing something embarrassingly obvious here?
Edit: I originally had the second equation as $ A = -2y^2 + 600y $ and I "fixed" it. Working too late and losing efficiency.
This leads to
$$-2y^2 + 600y = -x^2 + 300x $$ or $$2(y^2 - 300y) = (x^2 - 300x) $$
which produces a similar-looking graph and trivial (zero-area) results (among infinitely many): $(0,0), (0,300)$ and $(300,0)$.