related-to-Q-19333-the-side-lengthes-of-a-triangle-are-integer-if-the-perimeter-of-the-triangle-is-100-how-many-different-triangles-exist-what-is-the-maximum-area-of-them-

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Question Number 19388 by mrW1 last updated on 10/Aug/17

$$\mathrm{related}\mathrm{to}\mathrm{Q}.19333$$$$\mathrm{the}\mathrm{side}\mathrm{lengthes}\mathrm{of}\mathrm{a}\mathrm{triangle}\mathrm{are}$$$$\mathrm{integer}.\mathrm{if}\mathrm{the}\mathrm{perimeter}\mathrm{of}\mathrm{the}\mathrm{triangle}$$$$\mathrm{is}100,\mathrm{how}\mathrm{many}\mathrm{different}\mathrm{triangles}$$$$\mathrm{exist}?\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{maximum}\mathrm{area}\mathrm{of}$$$$\mathrm{them}?$$

Commented by mrW1 last updated on 10/Aug/17

$$\mathrm{I}\mathrm{think}{\mathrm{A}}_{\max }=340\sqrt{2}\mathrm{with}\mathrm{side}\mathrm{lengthes}$$$$34/33/33$$

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