In right triangle ABC, AC is the hypotenuse. If AC is 40 and AB + BC = 60, what is the area of the triangle ABC?  Choose the correct choice.
A) 225  B) 450  C) 25√2  D) 500  E) 200√2
Square AB + BC = 60:   (AB)^2 + 2*AB*BC + (BC)^2 = 3600. Since (AC)^2 = (AB)^2 + (BC)^2 = 40^2 = 1600, then (AB)^2 + 2*AB*BC + (BC)^2 = 1600 + 2*AB*BC = 3600.   1600 + 2*AB*BC = 3600.   AB*BC = 1000.   The area = 1/2*AB*BC = 500.   Answer: 500.
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In right triangle ABC, AC is the hypotenuse. If AC is 40 and AB + BC = 60, what is the area of the triangle ABC?