Original area = π(d/2)²
= (πd²) / 4

New area = π(2d/2)²
= πd²

Increase in area = (πd² - πd²/4)
= 3πd²/4

Correct Option: C

Original area = π(d/2)²
= (πd²) / 4

New area = π(2d/2)²
= πd²

Increase in area = (πd² - πd²/4)
= 3πd²/4

∴ Required increase percent
= [(3πd²)/4 x 4/(πd²) x 100]%
= 300%

Let the diagonal of one square be (2d) cm
Then, diagonal of another square = d cm

∴ Area of first square = [ 1/2 x (2d)²] cm²
Area of second square = (1/2 x d²) cm²

Correct Option: D

Let the diagonal of one square be (2d) cm
Then, diagonal of another square = d cm

∴ Area of first square = [ 1/2 x (2d)²] cm²
Area of second square = (1/2 x d²) cm²

∴ Ratio of area = (2d)²/ d²
= 4/1 = 4: 1

Length of the longest pole = √ [(10)² + (8)²] m

Correct Option: B

Length of the longest pole = √ [(10)² + (8)²] m
= √ 164 m
= 12.8 m

Let breadth = b, length = 2b
∴ Area of rectangle = 2b x b
= 2b²

As per question.
∵ (2b - 5 ) (b + 5 ) = 2b² + 75
⇒ 5b = 75 + 25
⇒ 5b = 100
∴ b = 100 / 5 = 20

Correct Option: C

Let breadth = b, length = 2b
∴ Area of rectangle = 2b x b
= 2b²

As per question.
∵ (2b - 5 ) (b + 5 ) = 2b² + 75
⇒ 5b = 75 + 25
⇒ 5b = 100
∴ b = 100 / 5 = 20

Hence, length of the rectangle =2b
= 2 x 20
= 40 cm.

Area = 1/2 x (Diagonal)²

Correct Option: B

Area = 1/2 x (Diagonal)²
= (1/2) x 5.2 x 5.2 cm²
= 13.52 cm²