Three 205

Three metallic bars of lengths 400 cm, 600 cm, and 720 cm are cut into equal pieces. Find the largest possible area of a square that can be made from any of the three bars.

Correct answer:

A =  1600 cm²

Step-by-step explanation:

$$\begin{gathered} a=400\text{cm} \\ b=600\text{cm} \\ c=720\text{cm} \\ 400=2^4\cdot 5^2 \\ 600=2^3\cdot 3\cdot 5^2 \\ 720=2^4\cdot 3^2\cdot 5 \\ \text{GCD}(400,600,720)=2^3\cdot 5=40 \\ x=GCD(a,b,c)=GCD(400,600,720)=40\text{cm} \\ A=x^2=40^2=1600{\text{cm}}^2 \end{gathered}$$

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