Question

Two square of the same size with side length 6 cm are cut along the diagonal and placed to make a single square. What is the side length of the new square?

• A. $6\sqrt{3}$ cm
• B. $6\sqrt{2}$ cm
• C. $3\sqrt{3}$ cm
• D. $3\sqrt{2}$ cm

Answer 1

The correct option is A $6\sqrt{3}$ cm

From the question,
The side of the square $=6$ cm
So, the area of the square $={\text{Side}}^2=6{\text{cm}}^2=36{\text{cm}}^2$

The area of the new square will be double of the area of the old square.
So, area of the new square $=2\times 36{\text{cm}}^2=72{\text{cm}}^2$
The side length of the square $=\sqrt{72}\text{cm}=6\sqrt{2}\text{cm}$