The perimeter of a triangle is 170 feet and the sides are in the ratio of 25: 14: 12. find the area of the triangle.

Let
x,y, and z the long sides of the triangle 

we know that

x+y+z=170 ft> equation 1
x/y=25/14> y=14x/25> equation 2
y/z=14/12> equation 3
x/z=25/12> z=12x/25> equation 4

substitute equation 2 and equation 4 in equation 1
x+[14x/25]+[12x/25]=170> multiply by 25 both sides
25x+14x+12x=4250
51x=4250
x=4250/51
x=250/3
y=14x/25> y=(250/3)*(14/25)> y=140/3
z=12y/14> (140/3)*12/14> z=40

Using Heron's formula,
Area of the triangle = √s (s-a) (s-b) (s-c)
where s is the semiperimeter
s=170/2> s=85 ft
Area=√85*[85-250/3]*[85-140/3]*[85-40]
Area=9.22*[1.67]*[38.33]*[45]> Area=26558.21 ft²

the answer is
26558.21 ft²