Answer
31.8 m .
Work Step by Step
The land is equilateral in shape.
Height of the triangle $= \sqrt (200^{2}-100^{2})=100\sqrt 3$
So, area $=\frac{1}{2}\times 200 \times 100\sqrt 3=100^{2}\times \sqrt 3\, m^{2}$
Let the base of the upper smaller triangle be (2B).
By comparison of 2 triangles,
$\frac{100\sqrt 3-h}{100\sqrt 3}=\frac{2B}{200}$
$2B=\frac{2}{\sqrt 3}\times (100\sqrt 3-h)$
Since the area of the upper triangle is two-third of the whole area,
$\frac{1}{2}\times (100\sqrt 3-h)\times \frac{2}{\sqrt 3}\times (100\sqrt 3-h)=\frac{2}{3}\times 100^{2} \times \sqrt 3$
or, $100\sqrt 3-h=100\sqrt 2$
or, $h=100\times (\sqrt 3-\sqrt 2)=31.8\,m$
