Question

Which triangle’s unknown side length measures 53sqrt units?

Answer 1

The answer is the one with 10 and 47 I just got it right

Answer 2

Which triangle’s unknown side length measures 53 sqrt units?

assuming they are right triangles
we know that
c²=a²+b²

case a) 6 and 91sqrt
c=√91
a=6
b=√53
so
a²+b²----> 6²+√53²----> 36+53----> 89
89 is not √91²

case b) 10 and 47sqrt
c=10
a=√53
b=√47
a²+b²----> 53+47----> 100
100 is equal to 10²------> is ok

case c) 34sqrt and 19sqrt
c=√53
a=√34
b=√19
a²+b²----> 34+19----> 53
53 is equal to √53²----> is ok

case d) 20 and 73sqrt
c=20
a=√73
b=√53
a²+b²----> √73²+√53²----> 126
126 is not 20²

the answers are
10 and 47sqrt
34sqrt and 19sqrt