General Questions

Let each side = x cm

Then, (x + 4 )² - x² = 60

⇒ x ² + 8x + 16 - x² = 60

∴ x = 5.5 cm

Length = (40 x 10 ) dm = 400 dm.

Breadth = (15 x 10 ) dm = 150 dm.

Area of veranda = (400 x 150 ) dm²

Area of one stone = (6 x 5 ) dm²

∴ Required number of stones = (400 x 150) /(6 x 5) = 2000

Perimeter = 2 x (36 + 21 ) m = 144 m

∴ Number of flagstaffs = 144 / 3 = 38

Area = 1/2 x (Diagonal)²

= (1/2) x 5.2 x 5.2 cm²

= 13.52 cm²

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.

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

∴ Ratio of area = (2d)²/ d²

= 4/1 = 4 : 1

Area of equilateral triangle = √3/4 a² = 4√3.

⇒ a² = 16

∴ a = 4 cm

Given that, a = 6 cm, b = 4 cm and c = 5 cm

Required perimeter = a + b + c

= 6 + 4 + 5 cm

= 15 cm

Given that, area = 10 sq cm,

Perpendicular = 20 cm and Base = ?

Area = (Base x Perpendicular) / 2

⇒ 10 = (Base x 20) / 2

∴ Base = 1 cm