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)   (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
===========================
Equation:
one leg = x
other leg = x+14
---------------------
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)
================================
Cheers,
Stan H.
Answer by Edwin McCravy(20055)   (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











Get 0 on the left:



Switch sides:



Divide through by 2



So we use the quadratic formula:

 

with a = 1 , , 

 

 









Make two fractions:





Only the plus sign gives a positive answer.

Answer:  or about 8.459624834 feet

Edwin
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