The hypotenuse of a right-angled triangle is 39 cm and the difference of other two sides is 21 cm. Then the area of the triangle is

Let vertices of the triangle be A,B,C

$$AB^{2} + BC^{2} = AC^{2} = 39^{2} = 1521$$ ........(1) 

Let $$(AB - BC)^{2} = AB^{2} + BC^{2} - 2(AB)(BC)$$.....(2)

Substitute equation (1) in equation (2)

$$21^{2} = 1521 - 2(AB)(BC) ($$Given $$AB - BC = 21)$$

$$441 = 1521 - 2(AB)(BC) \Rightarrow 1080 = 2 (AB)(BC) \Rightarrow (AB)(BC) = 540$$

Area of the triangle = $$\frac{1}{2}$$ x base x height = $$\frac{1}{2}(AB)(BC) = \frac{1}{2}(540) = 270$$

Hence, option B is the correct answer.