Question

If the diagonal of a square is doubled to make another square, the area of the new square will:

• A. become four-fold
• B. become two-fold
• C. become six-fold
• D. become eight-fold

Answer 1

The correct option is A become four-fold

We have to find out the area of the new square when the diagonal is doubled.

Now let the side of the square be $a$ and the of the diagonal be $D$.

From Pythagoras theorem,

$a^2+a^2=D^2$

$D^2=2a^2$

Now when $D$ becomes $2D$

$a_1^2+a_1^2=(2D{)}^2=4D^2$

$2a_1^2=4D^2$

$a_1^2=2D^2=4a^2$

Hence the area becomes 4 times than the previous area.

Option $\text{A}$ is the correct answer