Plates - gold

The father bequeathed to his two sons 4 gold plates in the shape of a square, which were 1 mm thick. The side lengths of these plates were 5 cm, 10 cm, 10 cm, and 15 cm. The sons were to receive the same amount of gold. How many gold plates did each son receive?

Final Answer:

a =  3
b =  1

Step-by-step explanation:

$$\begin{gathered} S_1=5^2=25{\text{cm}}^2 \\ {S}_2=10^2=100{\text{cm}}^2 \\ {S}_3=S_2=100{\text{cm}}^2 \\ {S}_4=15^2=225{\text{cm}}^2 \\ A=S_1+S_2+S_3=25+100+100=225{\text{cm}}^2 \\ a=3 \end{gathered}$$

$$\begin{gathered} B=S_4=225{\text{cm}}^2 \\ A=B \\ b=1 \end{gathered}$$

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