SOLUTION: The diagram of a right triangle shows 20 as the hypotenuse, 6x as a leg, and 2x as the other leg. Find x

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Question 949994: The diagram of a right triangle shows 20 as the hypotenuse, 6x as a leg, and 2x as the other leg.
Find x

Answer by MathLover1(20849) About Me  (Show Source):
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a right triangle shows 20 as the hypotenuse, 6x as a leg, and 2x as the other leg
if the hypotenuse is c, one leg a and the other leg b in a right triangle, using Pythagorean theorem, we have:
c%5E2=a%5E2%2Bb%5E2 ..........substitute given values
20%5E2=%286x%29%5E2%2B%282x%29%5E2
400=36x%5E2%2B4x%5E2
400=40x%5E2
400%2F40=x%5E2
10=x%5E2
x=+sqrt%2810%29 (note, we are looking for a leg, so we need only positive solution)
exact solutions:
one leg is: a=6x =>a=6sqrt%2810%29
and
the other leg is: b=2x =>b=2sqrt%2810%29
check:
20%5E2=%286sqrt%2810%29%29%5E2%2B%282sqrt%2810%29%29%5E2
400=36%28sqrt%2810%29%29%5E2%2B4%28sqrt%2810%29%29%5E2
400=36%2A10%2B4%2A10
400=360%2B40
400=400

approximate solution:
a=6sqrt%2810%29=>a=6%283.162277660168379%29=>a=18.97
b=2sqrt%2810%29=>b=2%283.162277660168379%29=>b=6.33
check:
c%5E2=a%5E2%2Bb%5E2
400=359.8609%2B40.0689=399.9298 round it to whole number
400=400