Question

A square is of area 200m square.A new square is formed in such a way that the length of its diagonals is
$\sqrt{2}$
times the given diagonal of the given square. Then the area of the new formed is....​

Answer 1

given :-

area of the square = 200m²

formula to find the area of a square = side²

➡ side² = 200m²

➡ side = √200

by Pythagoras theorem we get,

➡ diagonal² = (√200)² + (√200)²

➡ diagonal² = 200 + 200

➡ diagonal = √400

➡ diagonal = 20m

ATQ, a new square is formed in such a way that the length of its diagonals is √2 times the given diagonal of the given square.

therefore the diagonal of the new square is = 20√2m

again applying Pythagoras theorem,

➡ (20√2)² = side² + side²

➡ 800 = 2side²

➡ 800/2 = side²

➡ side = √400

➡ side = 20cm

the side of the new square is 20cm.

hence it's area = side × side

= 20 × 20

= 400cm²

the area of the new square formed is 400cm²

Answer 2

click on photo .

Answer is 400 cm .

Thanks .