Estimate the percentage of water consumption for domestic use if one person uses 100 liters/day and a family of 5 people uses 400 liters/day.

Let the two forces be $F_1$ and $F_2$.
Let the resultant force be $R$.
Given:

• The resultant force $R = 18 \, \text{N}$.
• One of the forces, let's call it $F_1 = 12 \, \text{N}$.
• The resultant $R$ is at right angles ($90^\circ$) to the smaller force.

Let's assume $F_1$ is the smaller force. This means the angle between the resultant $R$ and $F_1$ is $90^\circ$.
When the resultant of two forces is perpendicular to one of the forces, a right-angled triangle is formed by the three forces. The larger of the two original forces ($F_2$) acts as the hypotenuse, and the resultant ($R$) and the smaller force ($F_1$) act as the two legs.
Therefore, we can use the Pythagorean theorem:

$$F_2^2 = R^2 + F_1^2$$

We have $R = 18 \, \text{N}$ and $F_1 = 12 \, \text{N}$.

$$F_2^2 = (18 \, \text{N})^2 + (12 \, \text{N})^2$$ $$F_2^2 = 324 \, \text{N}^2 + 144 \, \text{N}^2$$ $$F_2^2 = 468 \, \text{N}^2$$ $$F_2 = \sqrt{468} \, \text{N}$$

To simplify $\sqrt{468}$:

$$468 = 4 \times 117 = 4 \times 9 \times 13 = 36 \times 13$$ $$F_2 = \sqrt{36 \times 13} \, \text{N}$$ $$F_2 = 6\sqrt{13} \, \text{N}$$

Now, let's verify our assumption that $F_1$ is the smaller force.
$F_1 = 12 \, \text{N}$.
$F_2 = 6\sqrt{13} \, \text{N}$. Since $\sqrt{13}$ is approximately 3.606, $F_2 \approx 6 \times 3.606 = 21.636 \, \text{N}$.
Since $12 \, \text{N} < 21.636 \, \text{N}$, our assumption that $F_1$ is the smaller force is correct.

The other force is $6\sqrt{13} \, \text{N}$.