[ Isosceles, inscribed, and circumscribed trapezoids ] [ Projections of the bases, sides, or vertices of a trapezoid ]

The height of an isosceles trapezoid, dropped from the vertex of the smaller base to the larger base, divides the larger base into segments that are in the ratio 2:3. How does the larger base relate to the smaller one?
Let $CH$ be the height of the isosceles trapezoid $ABCD$, dropped from the vertex $C$ of the smaller base $BC$ to the larger base $AD$. Let $DH = 2t$, $AH = 3t$. Drop a perpendicular $BQ$ from vertex $B$ to the base $AD$. From the equality of the right triangles $AQB$ and $DHC$, it follows that $AQ = DH = 2t$, and since $BCHQ$ is a rectangle, then

$$
BC = HQ = AD - DH - AQ = 5t - 2t - 2t = t
$$

Therefore, $\frac{AD}{BC} = \frac{5t}{t} = 5$.

## Answer

5.00

Problem