# The trapezoid diagonal is 6, it divides the trapezoid into two similar triangles. Find the length of the lower base of the trapezoid if the bigger base is 12?

Oct 9, 2017

$3$ units

#### Explanation:

As shown in the figures, $A D \mathmr{and} B C$ are the bases of the trapezoid $A B C D$,
As $A D$ is parallel to $B C$,
$\implies \angle B C D = \angle C A D = x$
Given that the diagonal $A C$ divides the trapezoid into two similar triangles, namely, $\Delta A B C , \mathmr{and} \Delta D C A$, and as $\angle A D C \ne \angle A B C$
$\implies \angle C A B = \angle A D C = y$
$\implies \frac{B C}{A C} = \frac{C A}{D A}$
$\implies \frac{B C}{6} = \frac{6}{12}$
$\implies B C = 3$