Right Triangle in DS

[oquiella]

80. What is the area of right angled triangle PQR?
(1) The hypotenuse QR = 16
(2) PQ = 8


Hello, below is the explanation they gave me but I assumed that a right triangle would always be 45-45-90 Is this a incorrect assumption that made me deem statement 1 a sufficient since you can use a^2+b^2=c^2 to get the the other two legs, Please explain

Explanation:
Statement 1 provides the value of the hypotenuse of the right triangle but no information about the base or the height; NOT SUFFICIENT.
Statement 2 only provides information about one side of the triangle; NOT SUFFICIENT.
Combining the statements, we have the value of one side and hypotenuse of the right triangle from which the third side and hence the area can be calculated; SUFFICIENT.
The correct answer is C;
both statements together are sufficient.

[theCEO]

80. What is the area of right angled triangle PQR?
(1) The hypotenuse QR = 16
(2) PQ = 8


Hello, below is the explanation they gave me but I assumed that a right triangle would always be 45-45-90 Is this a incorrect assumption that made me deem statement 1 a sufficient since you can use a^2+b^2=c^2 to get the the other two legs, Please explain

It is not correct to assume that right-angled triangles are always 45-45-90.
Right angled triangles have 1 90-degree angle and 2 angles that sum to 90 degrees
You can have 30-60-90, 10-80-90, etc.

We know a^2+b^2=c^2= 16^2
In order to know the area, we need the values of a and b since area= ab*1/2
Since we don't know a or b, statement 1 is not sufficient.