Wednesday, 2 October 2013

Least Perimeter

In triangle ABC, AB = AC and the lengths of the sides are integers. Let E be the mid point of BC. If the length of BE, AE & AB are in A.P., then find the least possible perimeter of triangle ABC. 
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Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, ...