Answer:
Width: 1694 cm or 16.94 m
Length: 1706 cm or 17.06 m
Step-by-step explanation:
1. Write out the known equations:
First, the equation for the perimeter of a rectangle:
[tex]Perimeter = 2(Width) + 2(Length)[/tex]
We also know that the rectangle is 12 cm longer than it is wide. This leads to the second equation:
[tex]Length=Width+12[/tex]
2. Solve the system of equations for width:
Since we know the length in terms of width, and we know the perimeter, we can plug these values into the equation for the perimeter. First, let's rearrange the equation for perimeter to solve for width:
[tex]Perimeter = 2(Width) + 2(Length)\\Perimeter-2(Length)=2(Width)\\2(Width)=Perimeter-2(Length)\\Width=\frac{Perimeter-2(Length)}{2}[/tex]
Now, plug in the known values (since there are 100 cm in one metre, I'm multiplying the perimeter of 68 m by 100 to convert to centimetres--the perimeter of 68 m is equal to 6800 cm):
[tex]Width=\frac{6800-2(Width+12)}{2}[/tex]
Now, solve the equation for width:
[tex]Width=\frac{6800-2(Width+12)}{2}\\2(Width)=6800-2(Width+12)\\2(Width)=6800-2(Width)-24\\2(Width)+2(Width)=6800-24\\4(Width)=6800-24\\4(Width)=6776\\Width=1694cm[/tex]
3. Solve for length using width:
Now that we know the width, we can easily solve for the length using our previously established equation for length, [tex]Length=Width+12[/tex], as shown:
[tex]Length=Width+12\\Length=1694+12\\Length=1706cm[/tex]
4. Convert to metres.
If you want to know the answer in metres, you can convert from centimetres by dividing by 100:
1694/100 = 16.94 m
1706/100 = 17.06 m
