What formula should i use? and how do i go about ?

QR = QP
QR = 10 so QP = 10
SR = SP
SP = 12 so SR = 12

You can find SQ by using the pythagorean theorem.
a^2 + b^2 = c^2.
In this case, a is QP, b is SQ, and c is SR.
QP = 10 = a
SR = 12 = c
SQ = b (unknown, this is what we have to find)

Plug in these values so you can start to solve.
10^2 + b^2 = 12^2

Simplify as much as possible.
10^2 = 100
12^2 = 144
100 + b^2 = 144

Isolate b.
Subtract 100 from both sides.
b^2 = 44
Find the square root of both sides.
b = 6.63 (rounded from 6.63324958071)

That's it, that's b.
b is SQ so SQ is 6.63 since b is 6.63.

Check your work:
a^2 + b^2 = c^2
10^2 + 6.63^2 = 12^2
100 + 43.9569 = 144
143.9569 = 144
This would be correct if it weren't rounded.

But the question wants the answer in simplest radical form, not an integer.
The answer is √44 before being simplified.
But since it wants simplest, that's what it'll get.
When the radicand has no square factors, it is in simplest form.
√44 = √2^2 • 11 = √11 • √2^2 = 2√11

So the answer, in simplest radical form, is 2√11.
In non-simplified form, it is √44.
In decimal form, it is 6.63324958071.
In rounded decimal form, it is 6.63.

One unique triangle, because those angles add up to 180, and that's how many degrees there are in one triangle.