SOLUTION: in a right triangle, the hypotenuse is longer than the other two sides by 10 cm and 80 cm respectively. Determine the length of the sides of the triangles using a complete algebrai

Algebra ->  Triangles -> SOLUTION: in a right triangle, the hypotenuse is longer than the other two sides by 10 cm and 80 cm respectively. Determine the length of the sides of the triangles using a complete algebrai      Log On


   

Question 679676: in a right triangle, the hypotenuse is longer than the other two sides by 10 cm and 80 cm respectively. Determine the length of the sides of the triangles using a complete algebraic solution
Answer by pmatei(79) About Me  (Show Source):
You can put this solution on YOUR website!
Pythagorean theorem: a%5E2+%2B+b%5E2+=+c%5E2, with c the hypotenuse.
a+=+c-10
b+=+c-+80
%28c-10%29%5E2+%2B+%28c-80%29%5E2+=+c%5E2
c%5E2+-+20c+%2B+100+%2B+c%5E2+-+160c+%2B+6400+=+c%5E2
c%5E2+-+180c+%2B+6500+=+0
%28c-50%29%28c-130%29+=+0
c-50=0 or c-130=0
c=50 or c=130
If c=50, then a=c-10=40 and b=c-80=-30. We cannot have negative numbers for side length.
Thus:
c=130
a=120
b=50