Help needed in finding the area of the square (tricky geometry question)

Question

I saw this question posted on Twitter, and I can't seem to find the answer to this -

I am stuck with this puzzle for over 2 hours now.

How would one go about trying to solve this and can anyone explain it in a simple way that anyone can understand.

Answer 1

Let $A$ be the rectangle comprised of the yellow, green and pink rectangles.
The ratio of {area of orange} to {area of $A$} is $1:3$. So the height of $A$ is $12$.
So the area of the square is $(4+12)^2=256$.

Answer 2

Let the central rectangle's width and height be $w$ and $h$ respectively. Then because all rectangles have the same area

• the yellow rectangle has height $2h$ and hence width $\frac12w$
• the orange rectangle has width $\frac32w$ and hence height $\frac23h=4$ (so $h=6$)
• the blue rectangle has height $\frac83h$ and hence width $\frac38w$

All this is inside a square, so we have the square side as $\frac83h=\left(\frac32+\frac38\right)w=\frac{15}8w=16$. Thus the square's area is $256$ and $w=\frac{64}{45}h=\frac{128}{15}$.