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Suppose we have an isosceles trapezoid whose length of the associated square is $20$ and the length of the hypotenuse of the triangles is $30$. I want to determine if it is possible to find the height of the triangles, I think no.

Taken from mathworld.

(Taken from http://mathworld.wolfram.com/IsoscelesTrapezoid.html.)

So in our case $a = 20$ and $c = 30$, we want to find $h$.

Suppose $x$ is the base of one of the triangles, note that $x$ can be free. Then $x^2 + h^2 = 30^2$ so simply pick two distinct such $x$ and then $h$ will not be unique.

Is this correct?

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  • $\begingroup$ Done, sorry my computer is under repair and I am writing from my mobile. $\endgroup$ Commented Aug 24, 2018 at 4:18
  • $\begingroup$ Thanks! You are right. $\endgroup$ Commented Aug 24, 2018 at 4:22

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I agree. Referring to the figure in http://mathworld.wolfram.com/IsoscelesTrapezoid.html, given just the measurements $a$ and $c$ you can make $h$ be anything between $0$ and $c$ and then solve for $x$ where $x$ is the length labeled $\frac12(b - a)$ in the figure.

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