The perimeter of a rectangular traffic sign is 106 inches. Also its length is 15 inches longer than its width. What is the length and the width of this sign?
The perimeter of a rectangular traffic sign is 106 inches. Also its length is 15 inches longer than its width. What is the length and the width of this sign ?
Let L = length and W = width
perimeter : 106 = 2L + 2W (1)
L = W + 15
L-W = 15 | *2
2L - 2W = 30 (2)
$$\\(1) \qquad 2L + 2W = 106 \\
(2) \qquad 2L - 2W = 30$$
$$\begin{array}{lrcl}
\hline
(1)+(2):& 4L &=& 136\\\\
& L &=& \dfrac{136}{4} \\\\
& \textcolor[rgb]{1,0,0}{L} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{34} } \\\\
\hline
& W &=& L - 15 \\\\
& W &=& 34 - 15 \\\\
& \textcolor[rgb]{1,0,0}{W} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{19} }
\end{array}$$
The perimeter of a rectangular traffic sign is 106 inches. Also its length is 15 inches longer than its width. What is the length and the width of this sign ?
Let L = length and W = width
perimeter : 106 = 2L + 2W (1)
L = W + 15
L-W = 15 | *2
2L - 2W = 30 (2)
$$\\(1) \qquad 2L + 2W = 106 \\
(2) \qquad 2L - 2W = 30$$
$$\begin{array}{lrcl}
\hline
(1)+(2):& 4L &=& 136\\\\
& L &=& \dfrac{136}{4} \\\\
& \textcolor[rgb]{1,0,0}{L} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{34} } \\\\
\hline
& W &=& L - 15 \\\\
& W &=& 34 - 15 \\\\
& \textcolor[rgb]{1,0,0}{W} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{19} }
\end{array}$$