In right triangle ABC, AC is the hypotenuse. If AC is 10 and AB + BC = 20, what is the area of the triangle ABC?
Select:  A) 225  B) 450  C) 75  D) 200  E) 200√2
Square AB + BC = 20:   (AB)^2 + 2*AB*BC + (BC)^2 = 400. Since (AC)^2 = (AB)^2 + (BC)^2 = 10^2 = 100, then (AB)^2 + 2*AB*BC + (BC)^2 = 100 + 2*AB*BC = 400.   100 + 2*AB*BC = 400.   AB*BC = 150.   The area = 1/2*AB*BC = 75.   Answer: 75.
<result>C</result>
In right triangle ABC, AC is the hypotenuse. If AC is 10 and AB + BC = 20, what is the area of the triangle ABC?