Required increment = 2a + [a² / 100] %

Correct Option: C

Required increment = 2a + [a² / 100] %
= 2 x 25 + [(25²)/100)] %
= 50 + (625/100)%
= 56.25%

Let the diagonals of the squares be 3x and 2x.
∴ Ratio of their areas = [(1/2) (3x²)] / [(1/2) (2x²)]

Correct Option: A

Let the diagonals of the squares be 3x and 2x.
∴ Ratio of their areas = [(1/2) (3x²)] / [(1/2) (2x²)] = 9/4

Diagonal of square = √2a [a = side]
4√2 = √2 a
a = 4 cm
Now, area of square = a² = (4²) = 16
Side of a square whose area is 2 x 16.
a₁² = 32
⇒ a₁ = √32 ⇒a₁4√2

Correct Option: A

Diagonal of square = √2a [a = side]
4√2 = √2 a
a = 4 cm
Now, area of square = a² = (4²) = 16
Side of a square whose area is 2 x 16.
a₁² = 32
⇒ a₁ = √32 ⇒a₁4√2

Now, diagonal of new square = √2a
= √2x 4 √2
= 8 cm

According to the question,
area = √3a²/4

Correct Option: A

According to the question,
area = √3a²/4
= √243 /4
⇒ a² = √81 x 3/√3
∴ a = √9
= 3 cm

AB = 60 m, BC = 40 m and AC = 80 m
∴ s = (60 + 40 + 80 ) / 2 m = 90 m
(s-a) = 90 - 60 = 30 m,
(s-b) = 90 - 40 = 50 m and
(s-c) = 90 - 80 = 10 m

∴ Area of Δ ABC =
√s(s-a)(s-b)(s-c)
= √90 x 30 x 50 x 10 m²
= 300√15 m²

Correct Option: C

AB = 60 m, BC = 40 m and AC = 80 m
∴ s = (60 + 40 + 80 ) / 2 m = 90 m
(s-a) = 90 - 60 = 30 m,
(s-b) = 90 - 40 = 50 m and
(s-c) = 90 - 80 = 10 m

∴ Area of Δ ABC =
√s(s-a)(s-b)(s-c)
= √90 x 30 x 50 x 10 m²
= 300√15 m²

∴ Area of parallelogram ABCD = 2 x area of Δ ABC
= 600√15 m²