A rectangle is divided into 25 smaller rectangles, the perimeters of 9 of which are known to us by the numbers in the figure (which is not drawn to scale).

What is the perimeter of the pink rectangle?

46
47
48
49
50

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The sum of the Xrectangles' perimeters is equal to the big rectangle's perimeter, since any two of them is in a different row and in a different column.

The sum of the Yrectangles' perimeters is equal to the big rectangle's perimeter, since any two of them is in a different row and in a different column.

So the perimeter of the big rectangle is $46+47+45+49+50=237$ .

From that the perimeter of the pink rectangle is: $237-(45+48+51+46)=\boxed{47}$