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The lengths of the sides of a triangle are in the ratio of 17:10:9. Find the lengths of the three sides if the area of the triangle is 576 squared centimeter.

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The ratio 17:10:9 is already in reduced form. To get the actual sizes of the sides of the triangle we assume a variable 'x' to be the cancelled factor such that the sides have 17x, 10x and 7x. The problem gave us the area of the triangle, 576 squared centimeters. With sides and area, we can form the equation using the heron's formula for the area of the triangle.
        A = sqrt {s(s-a)(s-b)(s-c)} where s is the semi-perimeter and                                                                                   a, b and c as sides of the triangle.
the semi-perimeter in the problem is (17x+10x+9x)/2=18x.
 Substituting the values on the formula, we get
       576 = sqrt {18x(18x-17x)(18x-10x)(18x-9x)}
       576 = 36x^2
Computing for x 
       x= sqrt{576/36}=4.
Thus, the sides are 68, 40 and 36.