Hello again, polakio92!

c) A rectangle is cut to form a square.

The perimeter of the rectangle is 54 cm, and the area of the cut-off piece is 36 cm².

What are the dimensions of the original rectangle? Code:

x y
* - - - - - * - - - *
| | |
| | |
x | | | x
| | |
| | |
* - - - - - * - - - *
x y

The perimeter of the rectangle is 54: .

The area of the cut-off piece is 36 cm²: .

Substitute [1] into [2]: .

. . which factors: .

. . and has roots: .

and has y-values: .

There are **two** solutions: .

The original rectangle was: .

Code:

12 3
* - - - - - * - - - *
| | |
| | |
12 | | | 12
| | |
| | |
* - - - - - * - - - *
12 3
1½ 24
* - * - - - - - - - - - - - - *
1½ | | | 1½
* - * - - - - - - - - - - - - *
1½ 24

Both of them satisfy the problem!