SOLUTION: Given a right triangle with sides of length a,b,and c and area, a^2 + b^2 – c^2. Find the ratio, c/b, the ratio of the legs of the right triangle.

Algebra ->  Pythagorean-theorem -> SOLUTION: Given a right triangle with sides of length a,b,and c and area, a^2 + b^2 – c^2. Find the ratio, c/b, the ratio of the legs of the right triangle.       Log On


   

Question 258737: Given a right triangle with sides of length a,b,and c and area, a^2 + b^2 – c^2. Find the ratio, c/b, the ratio of the legs of the right triangle.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
From the Pythagorean theorem,
1.a%5E2=b%5E2%2Bc%5E2
From the area of a triangle,
A=%281%2F2%29bh where b is the base, h is the height.
For a right triangle, b and h are the legs, in this case, b and c.
A=%281%2F2%29bc=a%5E2%2Bb%5E2-c%5E2
%281%2F2%29bc=a%5E2%2Bb%5E2-c%5E2
Use eq. 1 and substitute,
%281%2F2%29bc=%28b%5E2%2Bc%5E2%29%2Bb%5E2-c%5E2
%281%2F2%29bc=2b%5E2
bc=4b%5E2
bc%2Fb%5E2=4
c%2Fb=4