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
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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) (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 =
A =
A =
Factoring the numbers we get
A =
A =
A =
A =
A =
Since A = 576, and solving for r
576 =
Divide each side by 36
16 =
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
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