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 one side of triangle is x and other will be (21+x) {(difference between 2 side = 21cm)}

It is a right angle triangle. so.

$$H^2=P^2+B^2$$

$$39^2=x^2+\left(x+21\right)^2\ $$

$$39^2=x^2+x^2+441+42x\ $$

$$1521=2x^2+441+42x\ $$

$$2x^2+42x\ -1080=0$$

$$x^2+21x\ -540=0$$

$$\left(x+35\right)\left(x-15\right)=0$$

x = -36, 15

-36 is rejected because side of triangle can not be negative.

x = 15, (Perpendicular or height) = 15 cm

Other side (base of triangle) = x + 21 = 15 + 21 = 36 cm

We know, 

Area of right angle triangle = $$\frac{1}{2}\times\ base\times\ height$$

= $$\frac{1}{2}\times\ 36\times\ 15=270\ cm^2$$

Hence, Option D is correct.