A square is of area 200m2
. A new square is formed in such a way that the
length of its diagonal is √2 times of the diagonal of the given square. Then the
area of the new square formed is
Answers
According to question,
Side lenght of square=
200
=10
2
m
So, lenght of its diagonal =10
2
×
2
=20m
Length of diagonal of new square =20×
2
m
So, side length of new square =
2
20
2
=20m
Hence, area of new square =20m×20m=400m
2
Answered By
toppr
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girl
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