Answer:
The length and width of the deck will be 11 meters and 9 meters respectively.
Step-by-step explanation:
The length of the rectangular deck is [tex]l[/tex] meter and width is [tex]w[/tex] meter.
The perimeter of the deck should be 40 meters. So, the first equation will be...
[tex]2(l+w)= 40\\ \\ \Rightarrow l+w = 20 ..................................(1)[/tex]
The difference between twice the length and twice the width should be 4 meters. So, the second equation will be....
[tex]2l-2w= 4\\ \\ \Rightarrow l-w= 2 .................................(2)[/tex]
Adding equation (1) and (2), we will get.....
[tex](l+w)+(l-w)= 20+2\\ \\ 2l= 22\\ \\ l= \frac{22}{2}= 11[/tex]
Now plugging this [tex]l=11[/tex] into equation (1), we will get....
[tex]11+w= 20\\ \\ \Rightarrow w=20-11= 9[/tex]
So, the length and width of the deck will be 11 meters and 9 meters respectively.
