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.
Asked
Active
Viewed 243 times
0
-
1This doesn't have a definite answer - are the sides of the pond supposed to be integer numbers of metres? – Mark Bennet Nov 21 '17 at 07:58
1 Answers
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 $\frac{8 \sqrt{255}}{5} \simeq 25.6 m$.
Andreas
- 15,175