General right triangle

In a right triangle, if a =x+34 and b = x and c= 50, then solve for x. Side c is a hypotenuse. Then discuss the case when a or b is a hypotenuse.

Correct answer:

x =  14
X =  19.7647

Step-by-step explanation:

a = x+34 b = x c=50  c>a>b  c2 = a2+b2  502=(x+34)2+x2  −2x2−68x+1344=0 2x2+68x−1344=0 2 ...  prime number 68=22⋅17 1344=26⋅3⋅7 GCD(2,68,1344)=2  x2+34x−672=0  a=1;b=34;c=−672 D=b2−4ac=342−4⋅1⋅(−672)=3844 D>0  x1,2​=2a−b±D​​=2−34±3844​​ x1,2​=2−34±62​ x1,2​=−17±31 x1​=14 x2​=−48  x>0 x=x1​=14

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a>b>c a2 = b2+c2  (X+34)2= X2 + 502  68X−1344=0  68⋅ X−1344=0  68X=1344  X=681344​=19.76470588  X=17336​≐19.764706=19.7647

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