A square is constructed using the hypotenuse $\overline{ac}$ of right triangle $abc$ as a side, as shown below. find the area of

Question

Ilya [14]

3 years ago

10

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 $bc = 9$.

Mathematics

1 answer:

Arlecino [84] · Answer 1 · 2022-07-29T05:44:53+03:00

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