If the base of triangle PQR is 5, what is the perimeter of the triangl

If the base of triangle PQR is 5, what is the perimeter of the triangle?

Let Base = PQ,
(1) The area of triangle PQR is 12.5
--> 1/2*base*height = 12.5
--> 1/2*5*height = 12.5
--> Height = 5
--> Nothing can be said about the length of the other 2 sides --> Insufficient

(2) The length of a side of triangle PQR is 5∗√2
--> Nothing can be said about the length of the other 2 sides --> Insufficient

Combining (1) & (2),

base, PQ = 5, height = 5, one side = 5√2

Two possible cases
Case 1: An isosceles right angled triangle with 45-45-90 angles [PQ = 5, Height = PR = 5 & Hypotenuse, QR = 5√2]
Case 2: An obtuse triangle with base, PQ = 5, PR (obtuse angle = 135 deg) = 5√2, and 3rd side, QR = 5√5
--> Insufficient

IMO Option E