Answer:
[tex]A = 4500 ft^2[/tex]
Step-by-step explanation:
By definition:
The pre-meter P of a triangle ABC is equal to the sum of the length of its sides.
We know that:
[tex]P = 450\ ft\\AB = 9x\\BC = 41x\\CA = 40x[/tex]
The perimeter is:
[tex]P = AB + BC + CA\\P = 450 = 9x + 41x + 40x\\90x = 450\\x = 5[/tex]
Now we find the length of the sides:
[tex]AB = 45\\BC = 205\\CA = 200[/tex]
Once the length of the sides is known, we use Heron's formula to calculate the area.
First I find the semiperimeter S.
[tex]S = 0.5(45 + 205 +200)\\S = 225[/tex]
Then the Area is:
[tex]A = \sqrt{s(s-AB)(s-BC)(s-CA)}\\\\A = \sqrt{225(225-45)(225-205)(225-200)}\\\\A = 4500\ ft^2[/tex]