Final answer:
To triple the heat output from a stove element with constant voltage, the resistance must be reduced to one-third.
Step-by-step explanation:
The heat generated by a stove element varies directly as the square of the voltage (V) and inversely as the resistance (R). This relationship can be represented by the formula for electric power, P = V²/R. To triple the amount of heat generated while the voltage remains constant, the resistance needs to be reduced to a third of its original value. This is because the heat output is inversely proportional to the resistance. Reducing the resistance increases the current and thus increases the power dissipated as heat.