Hello, gabriel!

Your description is quite confusing.

I'll take a guess at what the diagram looks like.

$\displaystyle \text{A }5\times5\text{ square and a }3\times3\text{ square can be cut into pieces}$

. . . $\displaystyle \text{that will fit together to form a third square.}$

$\displaystyle \text{(a) Find the length of a side of the 3rd square.}$

$\displaystyle \text{(b) In the diagram mark }P\text{ on the segment }DC\text{ so that }PD = 3.$

. . . $\displaystyle \text{Then draw the segments }PA\text{ and }PF.$

. . . $\displaystyle \text{Calculate the lengths of these segments.}$

$\displaystyle \text{(c) Segments }PA\text{ and }PF\text{ divide the squares into pieces.}$

. . . $\displaystyle \text{Arrange the pieces to form the third square.}$

The area of the large square is: .$\displaystyle 5^2 = 25$ square units.

The area of the small square is: .$\displaystyle 3^2 = 9$ square units.

. . The area of the third square is: .$\displaystyle 25 + 9 \:=\:34$ square units.

Therefore, the side of the third square is $\displaystyle \sqrt{34}$ units.

I would guess that the diagram looks like this:

Code:

5
A o - - - - - - - - - o B
|* |
| * |
| * |
| * |
| * | 3
5 | * G o - - - - o F
| * | * |
| P * | * |
| * |* | 3
| * * | R |
| * * Q | |
o - - - - - o - - - o - - - - o
D 3 P 2 C 3 E

$\displaystyle PA$ and $\displaystyle PF$ are hypotenuses of right triangles with legs 3 and 5.

Hence, theire lengths are: .$\displaystyle \sqrt{3^2+5^2} \:=\:\sqrt{34}$

Move the pieces labeled $\displaystyle P,Q,R$ to their new locations.

Code:

*
* |*
* | *
* | *
* | *
* | R | *
* Q | | *
A o--------*----------o *
.* | P *
. * | *
. * | *
. * | *
. * G o-----------o F
. * | * .
. * | * .
. * | * .
. * |* .
. * * . .
. * * . .
. . . . . . o . . . . . . . . . .
P