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:

270 cm²

We know tht,

5,12 and 13 is a triplet.

And given,

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

So if we compare given hypotenuse with the triplet we get,

13x = 39

x = 3

Then,

5 = 5 × 3 = 15

12 = 12 × 3 = 36

So, difference between both of them = 36 - 15 = 21 ( satisfied.)

Area of right angled triangle = \(\frac{1}{2}\) × Base × Height

= \(\frac{1}{2}\) × 36 × 21 = 270 cm²