NCERT Book Class 8 Mathematics (Part II) Chapter 2

THE BAUDHĀYANA-
2 PYTHAGORAS THEOREM

2.1 Doubling a Square
In Baudhāyana’s Śulba-Sūtra (c. 800 BCE), Baudhāyana considers the
following question:

How can one construct a square having double the area
of a given square?
A first guess might be to simply double the length of
each side of the square. Will this new square have double
the area of the original square?
It’s not hard to see that the new square will have area 2 × 2 = 4 times
the area of the original square:

So how can one make a square that has double the area? Baudhāyana
in his Śulba-Sūtra (Verse 1.9) gave an elegant answer to this question:

The diagonal of a square produces a square of double the area of the
original square.

As Baudhāyana says, the key is to construct a square on the diagonal
of the original square: