Question

When two squares of the same size are joined to make a large square, find the length of the side of the large square.

• A. Same as the length of the side of the smaller square
• B. Double the length of the side of the smaller square
• C. The length of the diagonal of the smaller square
• D. The length of the diagonal of the larger square

Answer 1

The correct option is C

The length of the diagonal of the smaller square

Let the side of smaller square be 'x'.
Area $=x^2$
If two square of same size are combined, area of the larger square $=2x^2$
Side of the larger square $=\sqrt{2x^2}=\sqrt{2}x$
Diagonal of the smaller square $=\sqrt{x^2+x^2}=\sqrt{2x^2}=\sqrt{2}x$
So, side of the larger square = diagonal of the smaller square