A new square is built on the diagonal of the square, the area of which is 8. What is the side of the square?

1. Vertices of a given square A, B, C, D. AC – diagonal. Vertices of a square built on the diagonal A, C, K, M.

2. Calculate the length of the AC diagonal, which in the constructed square is its side.

For the calculation, we use the formula for the area (S) of this geometric figure:

S = AC x AC = AC².

AC = √S = √8 = 2√2 units.

3. Consider a right-angled triangle ACD, in which AC is the hypotenuse.

AC² = AD² + CD² (along the tower of Pythagoras).

The sides of the square are the same length. That is, AD = CD.

AC² = 2AD².

2AD² = (2√2) ² = 8.

AD² = 4.

AD = √4 = 2 units.

Answer: the length of the side of a given square is 2 units.

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