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.