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 wi

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)

$$\\(1) \qquad 2L + 2W = 106 \\ (2) \qquad 2L - 2W = 30$$

$$\begin{array}{lrcl} \hline (1)+(2):& 4L &=& 136\\\\ & L &=& \dfrac{136}{4} \\\\ & \textcolor[rgb]{1,0,0}{L} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{34} } \\\\ \hline & W &=& L - 15 \\\\ & W &=& 34 - 15 \\\\ & \textcolor[rgb]{1,0,0}{W} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{19} } \end{array}$$