Statement I is Insufficient:
QS is perpendicular to PR and length 12.
From this we can say that base of both triangles = QS=12. But, heights, PS and SR are still unknown to find
the area. Hence, it is insufficient.
Hence BCE
Statement II is Insufficient:
PQR perimeter is 60; with this information we may be able to find the side of PQR by the ratio of 3:4:5
since PQR is a right angled triangle. The sides should be 15, 20, and 25.
PR =25, since the hypotenuse is the greatest side.
Since we don’t know QS, and the length of PQ and QR.
This is also insufficient. Hence not B.
Combining the statement together.
If PQ is 15, QS=12 then PS is 9.
If PQ is 20, QS=12 then PS is 16.
Hence there are two answers and two ratios possible, it is insufficient. Basically, we don’t get whether
PQ>QR or QR>PQ.
Hence, it is not possible to find the ratios of areas.
Hence, the answer is E.