## Task 2 - 160512

On a straight line $g$, five points $A, B, C, D, E$ should be arranged in this order and satisfy the following conditions:

(1) The segment $A E$ has a length of $A E=18 \text{ cm}$.

(2) The segment $A D$ is $2 \text{ cm}$ shorter than the segment $A E$.

(3) The segment $C D$ has a length of $C D=5 \text{ cm}$.

(4) The segment $A B$ is $3 \text{ cm}$ longer than the segment $C E$.

a) Construct five such points $A, B, C, D, E$!

b) Determine the lengths of the segments $A D, A B, B C$!

As a solution, it is sufficient to provide:

a) a construction without description and

b) the determination of the segment lengths $A D, A B, B C$ from conditions (1) to (4).
From (2) and (1), we get $A D=16 \mathrm{~cm}$ and thus with (3) $A C=11 \mathrm{~cm}$.

Furthermore, $C E=A E-A C=18 \mathrm{~cm}-11 \mathrm{~cm}=7 \mathrm{~cm}$ and thus with (4) $A B=10 \mathrm{~cm}$.

For the segment lengths, it follows that:

$A D=16 \mathrm{~cm}, A B=10 \mathrm{~cm}, B C=A C-A B=11 \mathrm{~cm}-10 \mathrm{~cm}=1 \mathrm{~cm}$.

Construction:

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0072.jpg?height=57&width=1370&top_left_y=2162&top_left_x=343)