Quadratic equation problem involving rectangles

Question

In the centre of a rectangular lawn of dimensions $50 m \times 40 m$, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be $1184 m^2$ . Find the length and breadth of the pond.

Answer 1

I would interpret "in the centre" in such a way that the pond dimensions have to be proportional to the lawn. So the pond breadth is $50 \cdot x$ and its length is $40 \cdot x$ with some unknown factor $x$. So you have the pond area

$50 \cdot 40 \cdot x^2 = 2000 - 1184$

(hence the classification of the question as "quadratic") which gives $x = \sqrt{\frac{816}{2000}} = {\frac{\sqrt{255}}{25}}$. So the pond has sides $2 \sqrt{255} \simeq 31.9 m$ and $\frac{8 \sqrt{255}}{5} \simeq 25.6 m$.