SOLUTION: The hypotenuse of a right triangle is one meter longer than one leg and 3 meters longer than the other leg. How long is the hypotenuse?

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Question 1077231: The hypotenuse of a right triangle is one meter longer than one leg and 3 meters longer than the other leg. How long is the hypotenuse?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
h, hypotenuse
x and y legs
-
system%28h=x%2B1%2Ch=y%2B3%29
-
system%28x=h-1%2Cy=h-3%29

highlight_green%28h%5E2=%28h-1%29%5E2%2B%28h-3%29%5E2%29

h%5E2=h%5E2-2h%2B1%2Bh%5E2-6h%2B9
-2h-6h%2B10%2Bh%5E2=0
h%5E2-8h%2B10=0

h=%288%2B-+sqrt%2864-4%2A10%29%29%2F2
h=%288%2B-+sqrt%2824%29%29%2F2
h=%288%2B2%2Asqrt%286%29%29%2F2
highlight%28h=4%2Bsqrt%286%29%29