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

Rationale: 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 : e .
Answer: E