Question
A rectangle is divided into $16$ sub-rectangles as in the figure, the number in each sub-rectangle represents the area of that sub-rectangle. What is the area of the rectangle $K L M N$ ?



Area of rectangles are
$a c=10$
$b c=4$
$b d=12$
$d e=15$
$e f=25$
$\therefore \frac{a c}{b c} \times \frac{b d}{d e} \times e f =\frac{10}{4} \times \frac{12}{15} \times 25$
$\Rightarrow a f =50$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $X_i$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ |
| $f_i$ | $k+2$ | $2k$ | $K^{2}-1$ | $K^{2}-1$ | $K^{2}-1$ | $k-3$ |
where $\sum f_i=62$. if $[x]$ denotes the greatest integer $\leq x$, then $\left[\mu^2+\sigma^2\right]$ is equal $.........$.