the perimeter of a rectangle is 44cm. the length is 7 more then twice the width. what is the length/width?
width of the rectangle: W
length of the rectangle: L
the perimeter: $$p = 2 * ( L+W ) = 44\;cm \quad \mbox{or} \quad \boxed{L + W = 22 \;cm \qquad (1)}$$
the length is 7 more then twice the width: $$L = 7\;cm + 2W \quad \mbox{or} \quad \boxed{L - 2W = 7\;cm \qquad (2)}$$
$$\begin{array}{lrcl}
(1) - (2):&\\
&\underbrace{L-L}_{=0}+\underbrace{W-(-2W)}_{=3W}&=&\underbrace{22 cm - 7cm}_{=15\;cm}\\
&3W&=&15\;cm \quad | \quad : 3\\
&W&=&5\;cm
\end{array}$$
$$\begin{array}{rcl}
L + W &=& 22\;cm\\
L &=& 22 \;cm- W \\
L&=& 22\;cm- 5 \;cm\\
L &=& 17 \;cm
\end{array}$$
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