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 100 cm2 as shown in the second figure, then the area of the original square is ___. 50

Solution

## 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 = a2 Using Pythagorus theorem: Area of original square = a2 a2+a2=(length of diagonal)2 ⇒2a2=(length of diagonal)2 ⇒length of diagonal=a√2 The length of the new square = a√2 Area of new square  = (a√2)2=2a2 ∴ area of enlarged square is twice the area of small square. Given that the area of the larger square is 100 cm2 ⇒ The area of the original square is 50 cm2.

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