What is the relation between the lengths of the perpendicular sides of the triangle and area of the square?

The figure given below:

The area of a square with side as $\mathrm{BC}$ is the sum of areas of squares described on other two sides.

To make the area of the largest square $25$, what would be the sides of the smaller squares?

The figure given below:

The area of a square with side as $\mathrm{BC}$ is the sum of areas of squares described on other two sides.

To make the area of the largest square $41$, what would be the sides of the smaller squares?

What is the length in $\mathrm{cm}$ of the fourth side of the quadrilateral shown below?

The picture shows a plot of land in the form of a right-angled triangle joined to a square.

The total area of the plot is $2200$ square metres. What is its perimeter?

Some examples of Pythagorean triples are
 $3,4,5$ and $5,12,13$ and $8,15,17$.

Can you find some more?