Answer:
[tex]Area = 336\ m^2[/tex]
Step-by-step explanation:
If the ratio of the sides is 13:14:15, we can say that the length of each side is 13x, 14x and 15x.
Then, if the perimeter is 84 m, we have:
[tex]P = 13x + 14x + 15x = 84[/tex]
[tex]42x = 84[/tex]
[tex]x = 2[/tex]
The length of each side is:
[tex]13x = 26\ m[/tex]
[tex]14x = 28\ m[/tex]
[tex]15x = 30\ m[/tex]
Now, to find the area of the field, we can use the following formula:
[tex]Area = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where a, b and c are the sides and p is the semi perimeter:
[tex]p = P/2 = 42\ m[/tex]
So we have that:
[tex]Area = \sqrt{42(42-26)(42-28)(42-30)}[/tex]
[tex]Area = 336\ m^2[/tex]
