Question 143
In the drawing below, $ABCD$ is a rectangle and $E$ is the foot of the perpendicular drawn from $A$ to the diagonal $BD$. The distances from the point $E$ to the sides $DC$, $BC$ and $AB$ are $n$, $1$ and $x$, respectively. Let also $d$ be the length of the diagonal $BD$.
a) Verify that $DE = x^{2} \sqrt{1 + x^{2}}$.
b) Verify that $n = x^{3}$.
c) Verify that $d^{2/3} - n^{2/3} = 1$.
a) Verify that $DE = x^{2} \sqrt{1 + x^{2}}$.
b) Verify that $n = x^{3}$.
c) Verify that $d^{2/3} - n^{2/3} = 1$.