A3. Diagonals $A C$ and $B D$ of trapezoid $A B C D$ intersect at point $E$ and divide the trapezoid into 4 triangles with areas $25 \mathrm{~cm}^{2}, 36 \mathrm{~cm}^{2}, X \mathrm{~cm}^{2}$ and $X \mathrm{~cm}^{2}$ (see figure). What is the value of $X$?
(A) 25
(B) 30
(C) 32
(D) 36
(E) 61

![](https://cdn.mathpix.com/cropped/2024_06_07_21f8af0300261b15ee68g-06.jpg?height=263&width=505&top_left_y=1545&top_left_x=1415)
A3. Since triangles $A E D$ and $A B E$ have the same height from point $A$, it follows that $X: 36=|D E|:|E B|$. Similarly, triangles $C D E$ and $C E B$ have the same height from point $C$, so $25: X=|D E|:|E B|$. Therefore, $X: 36=25: X$, from which we calculate $X=\sqrt{25 \cdot 36}=30$.