Surface Area 436 cm²: Find Sides of Orthohedron with 20% Progressive Increase

First, we'll express $b$ and $c$ in terms of $a$:
$b = 1.2a \quad \text{and} \quad c = 1.44a$

Next, substitute these into the surface area formula for a cuboid:

$2(ab + bc + ca) = 436$

$ab = a \cdot (1.2a) = 1.2a^2$

$bc = (1.2a) \cdot (1.44a) = 1.728a^2$

$ca = (1.44a) \cdot a = 1.44a^2$

Substitute these into the formula:

$2(1.2a^2 + 1.728a^2 + 1.44a^2) = 436$

Simplify inside the parentheses:

$2 \cdot 4.368a^2 = 436$

$8.736a^2 = 436$

Solve for $a^2$:

$a^2 = \frac{436}{8.736}$

$a^2 \approx 49.93$

Taking the square root, we find:

$a \approx \sqrt{49.93} \approx 7.06$

Now, find $b$ and $c$:

$b = 1.2a = 1.2 \times 7.06 \approx 8.47$

$c = 1.44a = 1.44 \times 7.06 \approx 10.17$

Therefore, the dimensions of the orthohedron are:

$a = 7.06$, $b = 8.47$, and $c = 10.17$.