SOLUTION: the hypotenuse of a right triangle is 24 feet long. the lenght of one leg is 14 feet more than the other what is its length

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Question 243274: the hypotenuse of a right triangle is 24 feet long. the lenght of one leg is 14 feet more than the other what is its length
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the hypotenuse of a right triangle is 24 feet long. the lenght of one leg is 14 feet more than the other what is its length
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Equation:
one leg = x
other leg = x+14
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x^2 + (x+14)^2 = 24^2
2x^2 + 28x + 196 = 576
2x^2 + 28x - 380 = 0
x^2 + 14x - 190 = 0
x = [-14 +- sqrt(14^2 - 4*-190)]/2
x = [-14 +- sqrt(956)]/2
x = [-14 +- 30.92]/2
Positive solution:
x = 8.46 feet (one leg)
x + 14 = 22.46 feet (other leg)
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Cheers,
Stan H.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
the hypotenuse of a right triangle is 24 feet long. the lenght of one leg is 14 feet more than the other what is its length.

hypotenuse = c = 24
other leg = x 
one leg = x+14

c%5E2=a%5E2%2Bb%5E2

24%5E2=x%5E2+%2B+%28x%2B14%29%5E2

576=x%5E2%2B%28x%5E2%2B28x%2B196%29

+576+=x%5E2+%2B+x%5E2+%2B+28x+%2B+196+

576=2x%5E2%2B28x%2B196

Get 0 on the left:

0=2x%5E2%2B28x-380

Switch sides:

2x%5E2%2B28x-380=0

Divide through by 2

x%5E2%2B14x-190

So we use the quadratic formula:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

with a = 1 , b=14, c=-190

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

 

x+=+%28-14+%2B-+sqrt%28196%2B760%29+%29%2F2+

x+=+%28-14+%2B-+sqrt%28956%29+%29%2F2+

x+=+%28-14+%2B-+sqrt%284%2A239%29+%29%29%2F2+

x+=+%28-14+%2B-+2sqrt%28239%29+%29%29%2F2+

Make two fractions:

x+=+-14%2F2+%2B-+2sqrt%28239%29%2F2++

x=-7+%2B-+sqrt%28239%29

Only the plus sign gives a positive answer.

Answer: -7+%2B+sqrt%28239%29 or about 8.459624834 feet

Edwin