What is the perimeter of the rectangle formed by 7 separate squares with different sides? Explain how you arrived at your conclusion?

Question

Here is the the question:

you have 7 squares with sides 1, 2, 2, 2, 3, 4, 5. These squares form a rectangle with no gaps or overlaps. What is the perimeter of the rectangle formed

A) 34

B) 32

C) 31

D) 33

explain your answer

Answer 1

Let me try a different approach -
Add up the area of the squares to give $1+4+4+4+9+16+25=63$
The area of the rectangle is $63$ possible by $9*7$ or $3*21$ or$1*63$. The last two are not possible because we have a $5$ sided square. So, $9*7$. Which means perimeter is $32$.

Answer 2

Simple. Draw a $3$-square to the left and adjacent to the $4$-square, and squeeze a $1$-square on top of the $3$-square and adjacent to the $4$-square to fit in. Then stack $3$ $2$-squares on top of the $3$-square which are adjacent to the $1$-square, and finally place a $5$-square on top of both the $1$-square and the $4$-square to make the rectangle. Its length are width are: $3+2+2+2 = 9$, $3+4 = 7$. Thus the perimeter is $2(9+7) = 32$.