Question

A square of boundary 64 cm is given to us. If we remove a square of side 2 cm from one corner of the bigger square, the length of the new boundary ___.

• A. increases
• B. decreases
• C. remains the same
• D. cannot be determined

Answer 1

The correct option is C remains the same

Given that the boundary of a square is 64 cm.
$\therefore$ The side of the square is $\frac{64}{4}\text{cm}=16\text{cm}$ long.

Now, a square of side 2 cm is cut out from a corner of this larger square.


$\therefore$ The newly obtained figure has a boundary of length

$16\text{cm}+16\text{cm}+14\text{cm}+14\text{cm}+2\text{cm}+2\text{cm}=64\text{cm},$

which is equal to the boundary of the larger square.