SOLUTION: The length of one leg of a right triangle is 8 inches. The length of the other leg is 6 inches shorter than the hypotenuse. Find the length of the missing leg and the hypotenuse

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The length of one leg of a right triangle is 8 inches. The length of the other leg is 6 inches shorter than the hypotenuse. Find the length of the missing leg and the hypotenuse      Log On


   

Question 442534: The length of one leg of a right triangle is 8 inches. The length of the other leg is 6 inches shorter than the hypotenuse. Find the length of the missing leg and the hypotenuse
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Let c represent the hypotenuse in a right triangle. Let a,b be the legs.
Recall a^2 + b^2 = c^2
Let's select a to be 8 inches.
And let's let b = c-6, since b is 6 less than the hypotenuse.
Then:
8%5E2+%2B+%28c-6%29%5E2++=+c%5E2
64+%2B+c%5E2+-12c+%2B+36+=+c%5E2
-12c+%2B+100+=+0
4%28-3c+%2B+25%29+=+0
-3c+=+-25++=+c+=25%2F3
Since b = c-6, then b = 25/3 -6 = 7/3
Thus we have a=+8 b=+7%2F3 c=25%2F3