Question

what is the side length of square C if the three squares form a right triangle?

Answer 1

Since the area of square A is 97 square inches, then it follows that the sides of A are:

$a=\sqrt[]{97}$

And since the area of square B is 24 square inches, then it follows that the sides of B are:

$b=\sqrt[]{24}$

Then, we can note from the image that the side of C is the hypothenuse of a triangle with it's sides equal to a side of A and a side of B, then for the Pythagoras theorem we have that:

$c^2=(\sqrt[]{97})^2+(\sqrt[]{24})^2$

then

$c=\sqrt[]{121}$

where c is the length of the sides of C.

then the area of the triangle C is:

$\text{AreaC}=(\sqrt[]{121})^2=121\text{ square inches}$