Circumference 6598

Adam had three identical rectangles. He put them together and got a rectangle with a circumference of 50 cm. Then, he placed them differently and got a rectangle with a larger circumference. Calculate its perimeter.

Correct answer:

o₂ =  70 cm

Step-by-step explanation:

$$\begin{gathered} o_1=50\text{cm} \\ a=2b \\ {o}_1=3a+4b \\ a=2b \\ 50=3a+4b \\ a=2\cdot b \\ 50=3\cdot a+4\cdot b \\ a-2b=0 \\ 3a+4b=50 \\ Pivot:Row1\leftrightarrow Row2 \\ 3a+4b=50 \\ a-2b=0 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ 3a+4b=50 \\ -3.33b=-16.67 \\ b=\frac{-16.66666667}{-3.33333333}=5 \\ a=\frac{50-4b}{3}=\frac{50-4\cdot 5}{3}=10 \\ a=10 \\ b=5 \\ {o}_2=2\cdot b+6\cdot a=2\cdot 5+6\cdot 10=70\text{cm} \end{gathered}$$

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