A1. Nik placed some cubes next to each other so that their boundary faces touched each other, and on 3 boundary faces he wrote their areas (see the image). What is the area of the boundary face marked with $X$?
(A) 12
(B) 14
(C) 15
(D) 26
(E) None of the above.

![](https://cdn.mathpix.com/cropped/2024_06_07_21f8af0300261b15ee68g-10.jpg?height=417&width=465&top_left_y=894&top_left_x=1452)
A1. Let's denote some of the sides of the rectangles as $a, b, c$, and $d$ (see the figure).

![](https://cdn.mathpix.com/cropped/2024_06_07_21f8af0300261b15ee68g-25.jpg?height=474&width=529&top_left_y=740&top_left_x=775)

Then we have $a c=6, b c=15, b d=35$, and $a d=X$. Therefore, $a c \cdot b d=6 \cdot 35$ and simultaneously $b c \cdot a d=15 X$, so $6 \cdot 35=15 X$ and thus $X=14$.