SOLUTION: find the lengths of the sides of a triangle are in the ratio 17:10:9. find the lengths of the three sides if the area of the triangle is 576msquared

Algebra ->  Triangles -> SOLUTION: find the lengths of the sides of a triangle are in the ratio 17:10:9. find the lengths of the three sides if the area of the triangle is 576msquared      Log On


   

Question 814612: find the lengths of the sides of a triangle are in the ratio 17:10:9. find the lengths of the three sides if the area of the triangle is 576msquared
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
Heron's Formula for area is
A = sqrt(s(s-a)(s-b)(s-c) where s = (a + b + c)/2 with a,b,c being side lengths.
Since the side ratios are 17:10:9 we can write
rs = r(17+10+9)/2 = r*(36)/2 = r*18 = 18r where r is proportion factor
A = sqrt%2818r%2818r-17r%29%2818r-10r%29%2818r-9r%29%29
A = sqrt%2818r%28r%29%288r%29%289r%29%29
A = sqrt%2818%288%29%289%29r%5E4%29
Factoring the numbers we get
A = sqrt%282%2A3%2A3+%2A+2%2A2%2A2+%2A+3%2A3+r%5E4%29
A = sqrt%28+2%5E4+%2A+3%5E4+%2A+r%5E4+%29
A = 2%5E2+%2A+3%5E2+%2A+r%5E2
A = 4+%2A+9+%2A+r%5E2
A = 36+%2A+r%5E2
Since A = 576, and solving for r
576 = 36+%2A+r%5E2
Divide each side by 36
16 = r%5E2
So r = 4
This means that our side lengths are 4*17 , 4*10 , 4*9
The side lengths of our triangle are 68 , 40 , 36