It is known that the sum of the length, width, and height of a cuboid is 120 cm, and the ratio of length, width, and height is 5:4:3. If it is cut into two identical cuboids, how many square centimeters can the area be increased at most?
已知一个长方体长、宽、高的和是120厘米，长、宽、高的比是5：4：3，把它截成两个完全一样的长方体，面积最大可增加多少平方厘米．
<gadget id="calculator">5 + 4 + 3</gadget>
<output>12</output>

<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>

<gadget id="calculator">120 * (5/12)</gadget>
<output>50</output>

<gadget id="calculator">4 / 12</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">120 * (1/3)</gadget>
<output>40</output>

<gadget id="calculator">50 * 40 * 2</gadget>
<output>4_000</output>

<result>4_000</result>