1. ## Areas

A 5x5 square and a 3x3 square can be cut into pieces that will fit together to form a third square.
a. find the length of a side of the 3rd square
b. in the diagram mark P on the segment DC so that PD = 3, then draw the segments PA and PF. Calculate the lengths of these segments.
c. segments PA and PF divide the squares into pieces. Arrange the pieces to form the third square.
^what?! i dont get this

2. Originally Posted by gabriel
A 5x5 square and a 3x3 square can be cut into pieces that will fit together to form a third square.
a. find the length of a side of the 3rd square

how large is the side of a square that is made from 5x5 + 3x3 = 25 + 9 = 34 square units?

b. in the diagram mark P on the segment DC so that PD = 3, then draw the segments PA and PF. Calculate the lengths of these segments.
c. segments PA and PF divide the squares into pieces. Arrange the pieces to form the third square.
^what?! i dont get this

neither do I ... what diagram?
...

3. this is the diagram

segment AB is unknown
segment DC= 5 units
segment BC is unknown
^square 1
segment GF is unknown
segment CE= 3 units
segment FE= 3 units
segment GC is unknown
^square 2
*square 2 is adjacent to sqaure 1

4. Hello, gabriel!

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