We know that:

96, 110, and 146 make a Pythagoras triplet.

Area of a right angle triangle =

=

= 5280 m²

Therefore, required cost of levelling the field = 5280 × 5.60 = 29568 Rs.

Hence, option D is correct.

Let bigger side of rectangle be 4x cm.

Then, smaller side = (4x) ×  = 3x cm

Area of rectangle = 192 cm² (given)

⇒ (4x) × (3x) = 192

⇒ 12x² = 192

⇒ x² = 192/12 = 16

⇒ x =  = 4

Now, bigger side = 4 × 4 = 16 cm

And smaller side = 3 × 4 = 12 cm

Now, diagonal of rectangle (diameter of circle) =

 = 20 cm

Perimeter of circle = 2πr = 20π cm

The inner and outer radii of two concentric circles are 6.7 cm and 9.5 cm, respectively as shown in figure:

Difference between their circumferences =

∴ Ratio of area of two triangles

= (√5)² : (√7)²

= 5 : 7

Hence, option A is the correct answer.

Let the radius of circle be r metre

According to question,

Cost of fencing = 2420

⇒ 2πr × 11 = 2420

⇒  = 220

⇒ r = 35 m

Area of the field = πr² =  = 3850 m²

Hence, option A is the correct answer.

Let the sides are 3x, 4x and 5x

Now, according to question,

 5x – 3x = 3.6

 2x = 3.6

 x = 1.8 cm

Therefore, sides are 3x, 4x and 5x = 5.4cm, 7.2cm and 9cm

All three sides make a Pythagoras triplet, hence it is a right angle triangle

Area of right angle triangle =

=

= 19.44 cm²

Side of equilateral triangle = 16 cm

Area of equilateral triangle =  Side²

=  =  cm²

"Hence, option A is the correct answer."

Breadth of a rectangle = y unit

Area of a rectangle =

If length of a rectangle is increased to its three times and breadth is decreased to its half, then

New length of a rectangle = 3x unit

New breadth of a rectangle =  unit

Area of a rectangle =  =

Required ratio =

Let the radius of two circles are r_{1 and}

Now, according to question,

 r_{1 +}  = 286 cm …..eq1

area between two concentric circles =

 50336 =

 50336 =

  = 50336 ×

 () () = 16016

 () =

 () = 56 …..eq2

By adding both eq1 and eq2

 r_{1 +}  +  = 286 + 56

 2 = 342

  = 171 cm

By putting value of in eq1

 171 +  = 286

  = 286 – 171

  = 115 cm

Therefore, radii of two circles are 171 cm and 115 cm.

Area of room = Length × Width

= 12 × 8 = 96 cm²

The number of square designs required =  = 6