Circumference 6382

Jan bought a large rectangle plot with a circumference of 90 meters. He divided it into three rectangular plots. The shorter side has all three plots of the same length. Their longer sides are three consecutive natural numbers. Find out each plot's dimensions and the whole plot's area. Find all the solutions!

Correct answer:

a₁ =  3 m
a₂ =  6 m
a₃ =  9 m
S₃ =  324 m²

Step-by-step explanation:

$$\begin{gathered} 2a+2b=90 \\ a+b=45 \\ b=(x-1)+x+(x+1)=3x \\ a+3x=45 \\ a=3n,x=15-n,n=\dots 1,2,3\dots \\ {a}_1=3=3\text{m} \end{gathered}$$

$a_2=6=6\text{m}$

$$\begin{gathered} a_3=9\text{m} \\ {b}_1=45-a_1=45-3=42\text{m} \\ {b}_2=45-a_2=45-6=39\text{m} \\ {b}_3=45-a_3=45-9=36\text{m} \\ 3\cdot 13,3\cdot 14,3\cdot 15\text{m} \\ 6\cdot 12,6\cdot 13,6\cdot 14\text{m} \\ 9\cdot 11,9\cdot 12,9\cdot 13\text{m} \\ {a}_3=9=9\text{m} \end{gathered}$$

$$\begin{gathered} S_1=a_1\cdot b_1=3\cdot 42=126{\text{m}}^2 \\ {S}_2=a_2\cdot b_2=6\cdot 39=234{\text{m}}^2 \\ {S}_3=a_3\cdot b_3=9\cdot 36{\text{m}}^2=324{\text{m}}^2 \end{gathered}$$

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