the perimeter of a rectangle is 44cm. the length is 7 more then twice the width. what is the length/width?
+26367 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: $$L = 7\;cm + 2W \quad \mbox{or} \quad \boxed{L - 2W = 7\;cm \qquad (2)}$$
$$\begin{array}{lrcl}
(1) - (2):&\\
&\underbrace{L-L}_{=0}+\underbrace{W-(-2W)}_{=3W}&=&\underbrace{22 cm - 7cm}_{=15\;cm}\\
&3W&=&15\;cm \quad | \quad : 3\\
&W&=&5\;cm
\end{array}$$
$$\begin{array}{rcl}
L + W &=& 22\;cm\\
L &=& 22 \;cm- W \\
L&=& 22\;cm- 5 \;cm\\
L &=& 17 \;cm
\end{array}$$
+4473 Let's set up an equation after defining some variables:
L = length & W = width
L = 2W + 7 (length is 7 more than twice the width)
Perimeter of a rectangle is 2L + 2W...
2(2W + 7) + 2W = 44.
Distribute the 2.
4W + 14 + 2W = 44.
Combine like terms and subtract 14 from both sides.
6W = 30.
Solve for W.
W = 30/6 = 5.
So, L = 2W + 7 = 2(5) + 7 = 10 + 7 = 17.
L = 17 cm.
W = 5 cm.
Check: 2L + 2W = 44.
2(5) + 2(17) = 44.
10 + 34 = 44. Yes.
+26367 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: $$L = 7\;cm + 2W \quad \mbox{or} \quad \boxed{L - 2W = 7\;cm \qquad (2)}$$
$$\begin{array}{lrcl}
(1) - (2):&\\
&\underbrace{L-L}_{=0}+\underbrace{W-(-2W)}_{=3W}&=&\underbrace{22 cm - 7cm}_{=15\;cm}\\
&3W&=&15\;cm \quad | \quad : 3\\
&W&=&5\;cm
\end{array}$$
$$\begin{array}{rcl}
L + W &=& 22\;cm\\
L &=& 22 \;cm- W \\
L&=& 22\;cm- 5 \;cm\\
L &=& 17 \;cm
\end{array}$$
