Question 823533
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Hi
The hypotenuse of a triangle is 17 cm. 
The length of one leg is 1 cm less than twice the length of the other{{{highlight_green(x)}}}. 
Find the length of each leg: {{{highlight_green(x)}}}  and {{{highlight_green(2x-1)}}}
Applying the Pythagorean Theorem
  x^2 + (2x-1)^2 = 17^2 =289
   x^2 + 4x^2 - 4x + 1 = 289
         5x^2 - 4x - 288 = 0 
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (4 +- sqrt(5776 ))/(10) }}}
{{{x = (4 +- 76)/10 }}}
  x = -7.5, 8  (tossing out negative solution for unit measure
  x = 8cm  and the other leg is 15cm         {{{highlight_green(2x-1)}}}
CHECKING our answer***
  64 + 225 = 289