A rectangle has 15 cm as its length and 150 cm ² as its area .Its area is increased to 1 ¹ / ₃ times the original area by increasing only its length . Its new perimeter is?

Area of four walls = 2 x (l + b ) x h
? 2 x (7.5 + 3.5 ) x h = 77 m²
? h = 77 / (2 x 11) = 7/2
? h = 3.5 meters

Area of a four walls = 2(l + 8) x 6 = 168m²
? (l + 8) = 14
? l = 14-8
= 6 meters

Let the length, breadth and height of the room be l, b and h respectively

As per question
Cost of 2(l + b) x h = Rs. 48
? Required cost = cost of 2 (2l + 2b) x 2h
= cost of 4 [2(l + b) x h ]
= 4 x Rs. 48
= Rs. 192

Area of the plot = (3 x 1200) m²
= 3600 m²

Let breadth = y meters
Then Length = 4y meters,
Now area = 4y x y = 3600 m²
? y² = 900 m²
? y = 30 m

? Length of plot = 4y m
= (4 x 30) m
=120 m

Area of the square = (84 + 84) m²
Area of the rectangle = (144 x width) m²

From question both area would be same,
? Width = (84 x 84) / 144 m = 49 m

Let the width of the room be x members
Then, its area = (4x) m²

Area of each new square room = (2x)m²
Let the side of each new room = y meters
Then, y² = 2x
Clearly, 2x is a complete square when x=2
? y² = 4
? y = 2 m .

Let the side of the square = 100 m
So area of square = 100 x 100 = 10000.
New length = 140 m,
New breadth = 130 m

Increase in area = [(140 x 130) - (100 x 100)] m²
= 8200 m²

? Required increase percent = (8200/ 10000) x 100 % = 82%

Area of verandah = [(25 x 20) -(20 x 15)] m²
= 200 m²
? Cost of flooring = Rs. (200 x 3.50)
= Rs. 700

Area of the square field = 1 hectare
= 10000 m²

Side of the square = ? 10000 m = 100 m
Side of another square field = 100 + 1 = 101 m

? Required difference of area
= [(101)² - (100)²] m²
=[(101 + 100 ) (101 - 100) ] m²
= 201 m²

Let the area of square be (9x)² m² and (x²) m²

Then, their sides are (3x) m and x metres respectively
? Ratio of their perimeters = 12x / 4x
=3:1