SOLUTION: The hypotenuse of a right triangle is (x-2) and the sides are (2x-11) and (25-3x). Find the demensions of the triangle(find x first).

Question 36067: The hypotenuse of a right triangle is (x-2) and the sides are (2x-11) and (25-3x). Find the demensions of the triangle(find x first).
Answer by narayaba(40) (Show Source): You can put this solution on YOUR website!
using pythogrean theorem
hypotnuse^2 = side1^2 +side2^2
(x-2)^2 = (2x-11)^2 + (25-3x)^2
x^2 - 4x + 4 = 4x^2 -44x + 121 + 9x^2 -150x +625
12x^2 -190x + 742 = 0
using (-b +/- sqrt(b^2 -4*a*c))/(2*a) where a =12 b = -190 c =742
we get x = 7 or x = 212/24 = 53/6
if x =53/6 the the side 25-3x = 25 -53/2 = -3/2 which is not possible as the length of sides cannot be negative
hence x =7
hypotnuse = 7-2 =5
side1 = 2*7-11 = 3
side2 = 25 - 3*7 =4
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