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

Okay so n is going to represent our first number. since the second number of five times greater than n, the second number will be represented as 5n. for us to figure out the two  numbers we need to have  the value of n first. this is going to be done by adding the two numbers together, n and 5n. it can be simplified as 6n, which the problem states is equal to 72. divide 72 by 6n and you can solve for n.  n+5n=726n=72n=(72/6)n=12  now that we know the value of n, we have to multiply 5 times 12 which equals 60. so our two numbers/integers are 12 and 60