# Find the legs of isosceles triangle, given only the base

Is it possible to find the legs of isosceles triangle, given only the base length? I think that the info is insufficient. Am I right?

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Yes, a sketch or two shows that. –  André Nicolas Jun 5 '13 at 14:59

You are correct that it is impossible. Given only the base length of an isosceles triangle, we cannot determine the length of its sides: one would need to have the measure of the angle opposite the base in order to determine the lengths of the sides.

If the base of a triangle is fixed, an angle of smaller measure $m$ opposite the base would give longer congrent sides, than would an angle of greater measure. See for example, the following nested triangles:

For the same base $\overline{AC},\;m(\angle E) \lt m(\angle D) \lt m(\angle B)$, and $|CE|>|DE|> |BE|$.

You can experiment with a triangle of a given base, to see how the angle opposite the base determines the length of its sides.

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Neat applet! +1 –  Amzoti Jun 6 '13 at 0:40
@Amzoti I wish I could have posted it, here, in action! –  amWhy Jun 6 '13 at 0:43
@Amzoti I just uploaded an image from geogebra: I finally figured out that you can export graphics directly to image files (e.g., png) –  amWhy Jun 6 '13 at 1:18
@Amzoti Nice...I haven't explored the full power of WA, nor of my neglected Mathematica/Matlab software...(blame it on MSE - AGAIN) ;-) –  amWhy Jun 6 '13 at 1:24
Wow, I don't have either of those, and want Mathematica so bad! It is an amazing piece of SW!!!! Matlab is used by a lot of engineers as it has wonderful communications add-ons. –  Amzoti Jun 6 '13 at 1:25

The base length of an isosceles triangle is not enough to determine the triangle:

$\hspace{2cm}$

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Given the base langth $a$ any $b>\frac a2$ constitutes a valid leg length.

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