Question

Two lines are drawn parallel to the diagonal of a square as shown in the first figure. Another set of parallel lines are drawn along the second diagonal to form a larger square of the area $100c{m}^2$ as shown in the second figure, then the area of the original square is ___.

• A. 50

Answer 1

The correct option is A 50

Two lines are drawn parallel to the diagonal of a square and another set of parallel lines are drawn along the second diagonal to form a larger square, then the area of the larger square is double the area of the original square.
Let's assume length of original square is 'a'.
Area of original square = $a^2$
Using Pythagorus theorem:
Area of original square = $a^2$
$a^2+a^2=(\text{length of diagonal}{)}^2$
$\Rightarrow 2a^2=(\text{length of diagonal}{)}^2$
$\Rightarrow \text{length of diagonal}=a\sqrt{2}$
The length of the new square = $a\sqrt{2}$
Area of new square = $(a\sqrt{2}{)}^2=2a^2$
$\therefore$ area of enlarged square is twice the area of small square.

Given that the area of the larger square is $100c{m}^2$

$\Rightarrow$ The area of the original square is $50c{m}^2$.