Cubes

Surfaces of cubes, one of which has an edge of 42 cm shorter than the other, differ by 16128 cm². Determine the length of the edges of these cubes.

Final Answer:

a =  53 cm
b =  11 cm

Step-by-step explanation:

$$\begin{gathered} a-b=42 \\ \Delta S=S_1-S_2=16128 \\ 6a^2-6b^2=16128 \\ (42+b{)}^2-b^2-2688=0 \\ b=\frac{2688-42^2}{2\cdot 42}=11 \\ a=42+b=42+11=53\text{cm} \end{gathered}$$

$$\begin{gathered} b=11=11\text{cm} \\ \text{ Verifying Solution: } \\ {S}_1=6\cdot a^2=6\cdot 53^2=16854{\text{cm}}^2 \\ {S}_2=6\cdot b^2=6\cdot 11^2=726{\text{cm}}^2 \\ \Delta S=S_1-S_2=16854-726=16128{\text{cm}}^2 \end{gathered}$$

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