Rectangle

The length of the rectangle is 12 cm greater than three times its width. What dimensions and area does this rectangle have if its circumference is 104 cm?

Correct answer:

a =  42 cm
b =  10 cm
S =  420 cm²

Step-by-step explanation:

$$\begin{gathered} o=104\text{cm} \\ 2(a+b)=o \\ a=12+3b \\ 2(a+b)=104 \\ a=12+3b \\ 2\cdot (a+b)=104 \\ a=12+3\cdot b \\ 2a+2b=104 \\ a-3b=12 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a+2b=104 \\ -4b=-40 \\ b=\frac{-40}{-4}=10 \\ a=\frac{104-2b}{2}=\frac{104-2\cdot 10}{2}=42 \\ a=42 \\ b=10 \end{gathered}$$

$S=a\cdot b=42\cdot 10=420{\text{cm}}^2$

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