Questions on Geometry: Triangles answered by real tutors!

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Question 154288: The hypotenuse equals 23 units, find the size of the other two legs of a right triangle with one leg 3 units more than the other. What is the formula?: The hypotenuse equals 23 units, find the size of the other two legs of a right triangle with one leg 3 units more than the other. What is the formula?
Answer by orca(336) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the length of the shorter leg, then that of the longer one is x + 3.
Applying the Pythagorean Theorem, we have
x^2 + (x+3)^2=23^2
Solving for x, we have
x^2+x^2+6x+9=529
2x^2+6x-520=0
x^2+3x-260=0 (divide both sides by 2)
x = (-b +- sqrt( b^2-4*a*c ))/(2*a) (plug in a=1,b=3,c=-260)
x = (-(3) +- sqrt( 3^2-4*1*(-260) ))/(2*1)
x = (-3 +- sqrt( 9+1040 ))/2
x = (-3 +- sqrt( 1049 ))/2
So
x = (-3 + sqrt( 1049 ))/2 = 14.69
Or
x = (-3 - sqrt( 1049 ))/2=-17.69 (reject this solution as the length can not be negative)
Thus the length of the shorter leg is 14.69 units, and the length of the longer one is x+3=14.69+3=17.69 units