1. **Problem Statement:** Prove that for an ideal resistor (R), the area (cm) is related to the resistance and other parameters given that 1 cm = 0.7 (units not specified). 2. **Understanding the Problem:** The problem seems to involve the relationship between the physical dimensions (area) of a resistor and its resistance. Typically, resistance $R$ is related to resistivity $\rho$, length $L$, and cross-sectional area $A$ by the formula: $$ R = \frac{\rho L}{A} $$ 3. **Given:** - Area (cm) = function of something (not fully clear) - 1 cm = 0.7 (likely a conversion or scaling factor) - The resistor is ideal 4. **Assumptions:** - The length $L$ and resistivity $\rho$ are constants or known. - The 0.7 factor might be a scaling factor for the area or length. 5. **Proof Steps:** - Start with the resistance formula: $$ R = \frac{\rho L}{A} $$ - If 1 cm corresponds to 0.7 units in the problem's scale, then the effective length or area might be scaled by 0.7. - Suppose the actual area $A_{actual} = 0.7 \times A_{measured}$. - Substitute into the resistance formula: $$ R = \frac{\rho L}{0.7 A_{measured}} = \frac{1}{0.7} \times \frac{\rho L}{A_{measured}} $$ - This shows that the resistance is inversely proportional to the scaled area. 6. **Conclusion:** The relationship between resistance and area holds with the scaling factor 0.7 applied to the area or length, confirming the ideal resistor behavior under the given scaling. **Final answer:** The resistance $R$ is inversely proportional to the scaled area $A$ with factor 0.7, consistent with the ideal resistor formula.