Question

Show that no triangle has two sides each shorter than its corresponding altitude (from the opposite vertex).

Answer 1

Assume that $AD>BC$ and $BE>AC$

then $AD>BC\ge BE$ (Because hypotenuse of a right angled triangle is greater)

According to our assumption $BE>AC$

So, $AD>BC\ge BE>AC$

But, $AC\ge AD$

So, we got a contradiction.

Our assumption is not possible.