A thermometer shows a reading of 6.6 cm when measuring a child's temperature. The length between the 0°C and 100°C marks is 16.5 cm. What is the child's temperature?

The rise of the liquid above the lower fixed point ($L_T - L_0$) is $6.6 \text{ cm}$.
The length between the lower and upper fixed points ($L_{100} - L_0$) is $16.5 \text{ cm}$.
Assuming a Celsius scale, the lower fixed point is $0^\circ\text{C}$ and the upper fixed point is $100^\circ\text{C}$.

The formula for temperature ($T$) is:

$$T = \frac{L_T - L_0}{L_{100} - L_0} \times (T_{100} - T_0) + T_0$$

Since $T_0 = 0^\circ\text{C}$ and $T_{100} = 100^\circ\text{C}$, the formula simplifies to:

$$T = \frac{L_T - L_0}{L_{100} - L_0} \times 100^\circ\text{C}$$

$$T = 0.4 \times 100^\circ\text{C}$$ $$T = 40^\circ\text{C}$$

The child's body temperature is $\text{40}^\circ\text{C}$.