Question 1145973
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We have right angled triangle ABC with the right angle at vertex A.

 
The hypotenuse length is "a" units, and the leg AC has the length x (given).



(a)  Apply Pythagorean theorem :  | BC | = {{{sqrt(a^2-x^2)}}} = {{{sqrt(12^2-x^2)}}}.


     it is the expression you are looking for.




(b)  Area is half of the product of leg lengths


        A = {{{(1/2)*x*sqrt(12^2-x^2)}}}.



(c)  The domain of this function is  0 < x < 12.


      The endpoints 0 and 12 are not included to the domain, since otherwise the triangle becomes degenerated.
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