What is the area of a right-angled triangle PQR?

✓ Correct Answer: Option C

Let the legs be 'a' and 'b', and hypotenuse 'c'. Area = (1/2)ab. (1) a+b+c=30. Insufficient. (2) c=13. a^2+b^2=13^2=169. Insufficient. Combining, a+b+13=30 => a+b=17. We have (a+b)^2 = a^2+b^2+2ab => 17^2 = 169+2ab => 289 = 169+2ab => 2ab=120 => ab=60. Area = (1/2)ab = (1/2)*60 = 30. Sufficient.