The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and the breadth is increased by 5 cm, the area of the rectangle is increased by 75 cm ² . Therefore , the length of the rectangle is?

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

Perimeter = 2 x (36 + 21 ) m = 144 m
? Number of flagstaffs = 144 / 3 = 38

Let breadth = y meters,
Then, length = 2y meters

? Diagonal = ?y² + (2y)²
= ?5y² meters

So, ?5y² = 9 ?5
? y= 9

Thus, breadth = 9 m and length = 18 m
? Perimeter = 2 (18 + 9) m = 54m.

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

Let each side = x cm
Then, (x + 4 )² - x² = 60
? x ² + 8x + 16 - x² = 60
? x = 5.5 cm

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

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

Original area = ?(d/2)²
= (?d²) / 4

New area = ?(2d/2)²
= ?d²

Increase in area = (?d² - ?d²/4)
= 3?d²/4

? Required increase percent
= [(3?d²)/4 x 4/(?d²) x 100]%
= 300%

Ratio of area = a²/ ?(3/4) a²
= 4/?3 = 4:?3

Area of equilateral triangle = ?3/4 a² = 4?3.
? a² = 16
? a = 4 cm