Let the length and the breadth of the rectangle be 4x cm and 3x respectively.(4x)(3x) = 691212x² = 6912 x² = 576 = 4 * 144 = 2² * 12² (x > 0)
=> x = 2 * 12 = 24Ratio of the breadth and the areas = 3x : 12x² = 1 : 4x = 1: 96.

Let the breadth of the plot be b m.Length of the plot = 3 b m(3b)(b) = 8673b² = 867 b² = 289 = 17² (b > 0)b = 17 m.

Let the length and the breadth of the floor be l m and b m respectively.l = b + 200% of b = l + 2b = 3bArea of the floor = 324/3 = 108 sq ml b = 108 i.e., l * l/3 = 108l² = 324 => l = 18.

Length of the first carpet = (1.44)(6) = 8.64 cmArea of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)= 51.84(1.4)(5/4) sq m = (12.96)(7) sq mCost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40

Let the radii of the smaller and the larger circles be s m and l m respectively. 2∏s = 264 and 2∏l = 352 s = 264/2∏ and l = 352/2∏ Difference between the areas = ∏l² - ∏s² = ∏{176²/∏² - 132²/∏²} = 176²/∏ - 132²/∏ = (176 - 132)(176 + 132)/∏ = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m

Let the side of the square be a cm. Parameter of the rectangle = 2(16 + 14) = 60 cm
Parameter of the square = 60 cm i.e. 4a = 60 A = 15 Diameter of the semicircle = 15 cm Circimference of the semicircle = 1/2(∏)(15) = 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places

Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}² - ∏[4/2]² = ∏[2.25² - 2²]
= ∏(0.25)(4.25)  { (a² - b² = (a - b)(a + b) } = (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m

Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm. a² = 784 = (4)(196) = (2²).(14²) a = (2)(14) = 28 a = 2l, l = a/2 = 14 l = (7/3)s Therefore s = (3/7)(l) = 6
Circumference of the smaller circle = 2∏s = 12∏ cm.

Along one edge, the number of small cubes that can be cut = 100/10 = 10 Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000

Area of the square = s * s = 5(125 * 64)=> s = 25 * 8 = 200 cmPerimeter of the square = 4 * 200 = 800 cm.