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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 ___.


  1. 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=a2
The length of the new square = a2
Area of new square  = (a2)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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