In the diagram, the side lengths of four squares are shown. The area of the fifth square is $k$. What is the value of $k$ ?
(A) 64
(B) 49
(C) 36
(D) 25
(E) 16

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-039.jpg?height=352&width=415&top_left_y=2182&top_left_x=1321)
Let $s$ be the side length of the square with area $k$.

The sum of the heights of the squares on the right side is $3+8=11$.

The sum of the heights of the squares on the left side is $1+s+4=s+5$.

Since the two sums are equal, then $s+5=11$, and so $s=6$.

Therefore, the square with area $k$ has side length 6 , and so its area is $6^{2}=36$.

In other words, $k=36$.