Find the legs of isosceles triangle, given only the base

Question

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?

Answer 1

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.

Answer 2

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

Answer 3

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

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Answer 4

You will always need three data to determine a triangle. It can be any combination of angles, lengths, heights...

In your example, since you know it's an isosceles triangle, you'll have three data once you define an angle or a length apart from the base's length, because you know both angles at the base's ends are equal.

So, if you have the segment AB being the base of an isosceles triangle, once you know either angle C, height from base to C, length BC or length AC, you'll have everything you need.