In right triangle ABC, AC is the hypotenuse. If AC is 50 and AB + BC = 70, what is the area of the triangle ABC?
Choose the correct choice from the following answers:
A) 225 B) 450 C) 25√2 D) 200 E) 600
Square AB + BC = 70:   (AB)^2 + 2*AB*BC + (BC)^2 = 4900. Since (AC)^2 = (AB)^2 + (BC)^2 = 50^2 = 2500, then (AB)^2 + 2*AB*BC + (BC)^2 = 2500 + 2*AB*BC = 4900.   2500 + 2*AB*BC = 4900.   AB*BC = 1200.   The area = 1/2*AB*BC = 600.   Answer: 600.
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In right triangle ABC, AC is the hypotenuse. If AC is 50 and AB + BC = 70, what is the area of the triangle ABC?