Hello, aznmartinjai!

A square measuring 10 centimeter on a side

is divided by a vertical and a horizontal line segment

into rectangles with area of 12, 18, 28, and 42 cm².

Where should the vertical and horizontal lines be located? .Draw a diagram. Code:

x 10-x
* - - - * - - - - - *
| | |
y | 12 | 18 | y
| | |
* - - - + - - - - - *
| | |
| | |
10-y | 28 | 42 |
| | |
| | |
* - - - * - - - - - *

In the upper-left, we have a rectangle: .xy .= .12 . **[1]**

In the upper-right, another rectangle: .y(10 - x) .= .18 .**[2]**

From [2], we have: .10y - xy .= .18

. . . . . . . . . . . . . . . . . . .↓

Substitute [1]: . . . 10y - 12 .= .18 . → . 10y = 30 . → . **y = 3**

Substitute into [1]: .x·3 = 12 . → . **x = 4**

The solution looks like this: Code:

4 6
* - - - * - - - - - *
| | |
3 | 12 | 18 |
| | |
* - - - + - - - - - *
| | |
| | |
7 | 28 | 42 |
| | |
| | |
* - - - * - - - - - *