Hello, 

Here I am providing you with link for complete proof for the problem you asked

https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.meritnation.com/ask-answer/question/prove-that-the-area-of-a-right-angled-triangle-of-given-hypo/application-of-derivatives/2885836&ved=2ahUKEwjq74Df4NnfAhWVYisKHZI0DQ0QFjAIegQIBRAB&usg=AOvVaw1QFP0tufOgu1ipxMYH0fsP&cshid=1546798454523

Hope this helps ...