SOLUTION: If the altitude drawn to the hypotenuse of a right triangle EFG partitions it into two segments of lengths of 8 and 10, then find the length of the longer leg of triangle EFG in si

Algebra ->  Triangles -> SOLUTION: If the altitude drawn to the hypotenuse of a right triangle EFG partitions it into two segments of lengths of 8 and 10, then find the length of the longer leg of triangle EFG in si      Log On


   

Question 1158306: If the altitude drawn to the hypotenuse of a right triangle EFG partitions it into two segments of lengths of 8 and 10, then find the length of the longer leg of triangle EFG in simplest radical form.
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
We want to find y:




Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


By similar triangles, the length of the altitude to the hypotenuse of a right triangle is equal to the geometric mean of the lengths of the two segments of the hypotenuse:

h+=+sqrt%288%2A10%29 or h%5E2+=+8%2A10+=+80

Then the length of the longer leg of triangle EFG is

sqrt%28%2810%5E2%29%2Bh%5E2%29+=+sqrt%28100%2B80%29+=+sqrt%28180%29+=+6%2Asqrt%285%29