In a trapezium, the lengths of the two parallel sides are $6$ and $10$ units. If one of the oblique sides has length $1$ unit, then find the length of the other oblique side.
Using the short parallel side given, I split the opposite parallel side of $10$ units to $6, 2, 2$ units, the $2$ units being $4$ units remaining after subtraction divided equally to rest of the two parts of the side. I applied Pythagoras' theorem to the given oblique side and the $2$ units, such that, $1 = (4 + x^{2})^{\frac{1}{2}}$, but here, $x$ is square root of $-3$.
So, instead of splitting the $4$ units equally, I split them as $1$ and $3$ units & $0$ and $4$ units. But it does not work.
How do we solve the problem?
Thanks in advance.
Best Answer
Produce non-parallel sides until they meet, let the extended length of segment be x.By considering proportion in similar triangles of corresponding sides,
$$ \dfrac{x}{x+1} = \dfrac{6}{10} = \dfrac{3}{5}; \rightarrow x =1.5 $$
EDIT1:
We cannot go further beyond this towards the portion of traversal ( other oblique side ) which cannot be determined.