Which triangle’s unknown side length measures 53sqrt units? a. 6 and 91sqrt (sides of the triangle) b. 10 and 47sqrt c. 34sqrt and 19sqrt d.20 and 73sqrt

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