Area of a square inscribed in a triangle?

Question

Construct a triangle ABC whose base AB is 24 and altitude CH is 16.

Hence, inscribe a square EPGF (one of whose sides lies along AB) and calculate its area.

My book suggests to use triangle similarity. Please help me to solve it. Thanks in advance.

There are 3 approaches here, I think Saptrashi's answer would be best for you, http://math.stackexchange.com/questions/532122/maximum-area-of-a-square-in-a-triangle/708192#708192 — Sawarnik, May 10 '14 at 14:49

score 1 · Answer 1 · edited Jul 13 '15 at 16:29

1

$\triangle ABC\sim \triangle FGC$, hence $$\frac{AB}{CH} = \frac{FG}{CH-PG}$$

edited Jul 13 '15 at 16:29

answered May 10 '14 at 14:18

Hagen von Eitzen

1 Answers1