Chapter 1.2, Problem 43E

To determine

To calculate: The dimensions of the Norwegian flag whose perimeter is $190\text{inches}.$

Answer to Problem 43E

The dimensions of the Norwegian flag is $55in.by40in.$

Explanation of Solution

Given information :

Given perimeter of the Norwegian flag is $190\text{inches}.$

  

Since the Norwegian flag in shape of rectangle, whose perimeter is given by $\begin{array}{l}P=2\left(l+w\right)\\ wherel=\text{length}andw=\text{width}\end{array}$

Given $\text{length}\left(\text{l}\right)\text{=}\frac{11y}{8}\mathrm{inches},\text{width}\text{=y}\text{inches }\text{and}\text{perimeter}\left(P\right)=190\text{inches}\text{.}$

  $\begin{array}{l}\text{Thus,}\text{perimeter}\left(P\right)=2\left(\frac{11y}{8}+y\right)\\ \Rightarrow 190=2\left(\frac{11y}{8}+y\right)\\ \Rightarrow 95=\left(\frac{11y}{8}+y\right)\\ \Rightarrow 95=\left(\frac{11y+8y}{8}\right)\end{array}$

  $\begin{array}{l}\Rightarrow 95=\frac{19y}{8}\\ \Rightarrow y=\frac{8}{19}\times 95\\ \therefore widthy=40in.\\ \Rightarrow length\left(l\right)=\frac{11y}{8}=\frac{11}{8}\left(40\right)=55in.\\ \therefore length=55in.\end{array}$

Hence, the dimensions of the Norwegian flag is $55in.by40in.$