Question

A square is constructed using the hypotenuse $\overline{ac}$ of right triangle $abc$ as a side, as shown below. find the area of the square if $ab = 5$ and $bc = 9$.

Answer 1

see the picture attached to better understand the problem

we know that
Applying the Pythagoras Theorem
AC²=AB²+BC²-----> AC²=5²+9²----> AC²=25+81----> AC²=106
AC=√106 units

the length side of the square is equal to the hypotenuse
so
b=√106 units
where b is the length side of the square
area of the square=b²-----> (√106)²-----> Area=106 units²

the answer is
106 units²