SOLUTION: In the movie, "The Wizard of Oz," the Wizard says, "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side."
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Question 133166: In the movie, "The Wizard of Oz," the Wizard says, "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side."
Is his statement correct?
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
No, sides x,x,p with angles theta, theta, and 180 - 2*theta
x/sin(theta) = p/sin(180 - 2*theta)
p = xcos(theta)
sqrt(x) + sqrt(x) = sqrt(xcos(theta))
(sqrt(x) + sqrt(x))^2 = xcos(theta)
4x = xcos(theta)
0 = xcos(theta) - 4x
0 = x(cos(theta) - 4)
x = 0 which results in no triangle or cos(theta) = 4 which is impossible
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