Solution:
Consider the following diagram of the rectangular park given in the problem:
now, the perimeter P of this figure is the sum of all its sides, that is:
[tex]P\text{ = 2L + 2W}[/tex]But, the length of the park is 10,729.1 inches longer than the width, that is:
EQUATION 1:
[tex]L\text{ = 10729.1+W}[/tex]Substituting the above expression into the perimeter equation, we get:
[tex]P\text{ = 2 (10729.1 + W) + 2W}[/tex]this is equivalent to:
[tex]P\text{ = 2 (10729.1) + 2W + 2W}[/tex]this is equivalent to:
[tex]P\text{ = 21458.2 +4W}[/tex]But P = 23083.1 inches, then replacing this data into the previous equation, e get:
[tex]23083.1\text{= 21458.2 +4W}[/tex]solving for 4W, we get:
[tex]\text{ 4W = }23083.1-\text{21458.2}=\text{ 1624.9}[/tex]solving for W, we get:
[tex]\text{ W = }\frac{\text{1624.9}}{4}=406.2[/tex]now, replacing the above result into equation 1, we get:
[tex]L\text{ = 10729.1+W = 10729.1+}406.2\text{ = 11135.3}[/tex]so that, we can conclude that the correct answer is:
[tex]L\text{ = 11135.3}[/tex]
