SOLUTION: God bless you and hope you will clear my frustration to this nagging and seemingly wrong formula. We have a triangle with sides a, b and c with c as base, which is divided into two

Algebra ->  Triangles -> SOLUTION: God bless you and hope you will clear my frustration to this nagging and seemingly wrong formula. We have a triangle with sides a, b and c with c as base, which is divided into two      Log On


   



Question 393628: God bless you and hope you will clear my frustration to this nagging and seemingly wrong formula. We have a triangle with sides a, b and c with c as base, which is divided into two parts in r to s ratio, by altitude denoted by h. I.e. side a is hypoteneuse to r and side b to s. Is there a formula which runs as, h = [a * s + b * r] / r + s. Many engineers vehemently declared the wrongness of the formula

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
No, there is no such formula. A counterexample would suffice.
Let h = 1, r = 3, and s = 2.
==> c = r + s = 5.
Then a+=+sqrt%283%5E2+%2B+1%5E2%29+=+sqrt%2810%29, and
b+=+sqrt%282%5E2+%2B+1%5E2%29+=+sqrt%285%29. Then
, to 2 decimal places. But obviously this is not equal to h = 1.