Dimensions 3

A perimeter of a rectangular field is 96 meters. The length is four meters less than three times the width. Find the length and width (its dimensions).

Correct answer:

a =  35 m
b =  13 m

Step-by-step explanation:

$$\begin{gathered} p=96\text{m} \\ a=3\cdot b-4 \\ 2\cdot (a+b)=p \\ a=3\cdot b-4 \\ 2\cdot (a+b)=96 \\ a-3b=-4 \\ 2a+2b=96 \\ Pivot:Row1\leftrightarrow Row2 \\ 2a+2b=96 \\ a-3b=-4 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a+2b=96 \\ -4b=-52 \\ b=\frac{-52}{-4}=13 \\ a=\frac{96-2b}{2}=\frac{96-2\cdot 13}{2}=35 \\ a=35 \\ b=13 \end{gathered}$$

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