SOLUTION: Hi, trying to help my son grd 8 solve a question the hypotenuse of a right triangle is square root of 18....what are the lenghts of the legs of the triangle ?? that is all the i

Algebra ->  Pythagorean-theorem -> SOLUTION: Hi, trying to help my son grd 8 solve a question the hypotenuse of a right triangle is square root of 18....what are the lenghts of the legs of the triangle ?? that is all the i      Log On


   

Question 498590: Hi, trying to help my son grd 8 solve a question
the hypotenuse of a right triangle is square root of 18....what are the lenghts of the legs of the triangle ??
that is all the info we are given.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You must have been given more information about the right triangle.
Look!
a%5E2%2Bb%5E2+=+c%5E2 In this case, c+=+sqrt%2818%29 so c%5E2+=+18. Now we have:
a%5E2%2Bb%5E2+=+18 This equation has an infinite number of solutions unless you place some restrictions on a and b.
Let's assume the the numbers a and b must be integers (not an unreasonable assumption), then a and b can only take on the values of highlight%28a+=+3%29 and highlight%28b+=+3%29, so you'd get:
3%5E2%2B3%5E2+=+18 or
9%2B9+=+18
This implies that the triangle is an isosceles right triangle.
No other integers for a and b would work.