Right triangle

A right triangle has a hypotenuse of 10 m and a perimeter of 24 m. In square meters, what is the area of the triangle?  

Since the hypotenuse is an integer and the perimeter is an integer, the other two legs must be integers too. 

Just by recognition, a Pythagoras Triple of 6-8-10 will work.  That makes the area (1/2)(6)(8) = 24 meter²  

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Call the legs a, b

a + b + 10  = 24

a + b  =14      square both sides

a^2 + 2ab +b^2  =  196         { a^2 + b^2    = 10^2 = 100}

a^2 + b^2   + 2ab =  196

100 + 2ab = 196

2ab = 96

ab = 48

Area  =  (1/2)ab  =  24