Area of the room =(544 x 374) cm²
size of largest square tile = H.C.F. of 544 & 374
= 34 cm

Correct Option: B

Area of the room =(544 x 374) cm²
size of largest square tile = H.C.F. of 544 & 374
= 34 cm

Area of 1 tile = (34 x 34) cm²

∴ Least number of tiles required
= (544 x 374) / (34 x 34) = 176

Ratio of similar triangle
= Ratio of the square of corresponding sides
= (3x)² / (4x)² = 9x² / 16x²
= 9/16 = 9 : 16

Correct Option: C

Ratio of similar triangle
= Ratio of the square of corresponding sides
= (3x)² / (4x)² = 9x² / 16x²
= 9/16 = 9 : 16

Let there be n sides of the polygon. Then it has n vertices.
The total number of straight lines obtained by joining n vertices by talking 2 at a time is ⁿC₂
These ⁿC₂ lines also include n sides of polygon.
Therefore, the number of diagonals formed is ⁿC₂ - n.
Thus, ⁿC₂ - n = 44

Correct Option: C

Let there be n sides of the polygon. Then it has n vertices.
The total number of straight lines obtained by joining n vertices by talking 2 at a time is ⁿC₂
These ⁿC₂ lines also include n sides of polygon.
Therefore, the number of diagonals formed is ⁿC₂ - n.
Thus, ⁿC₂ - n = 44
⇒ [n(n - 1)/2] - n = 44
⇒ ( n² - 3n) / 2 = 44
⇒ n² - 3n = 88
⇒ n² - 3n - 88 = 0
⇒(n - 11) (n + 8) = 0
∴ n = 11

Let the radius of circle is 'r' and a side of a square is 'a',
then given condition
2πr = 4a
⇒ a = πr/2

∴ Area of square = (πr/2)² = π² /4r² = 9.86r²/4 = 2.46r²
and area of circle = πr² = 3.14;r²
and let the side of equilateral triangle is x.
Then, given condition,
3x = 2πr
⇒ x = 2πr/3

∴ Area of equilateral triangle = √3/4 x ²
= √3/4 x 4π²r²/9
= π²/3√3r²
= 1.89r²

Correct Option: A

Let the radius of circle is 'r' and a side of a square is 'a',
then given condition
2πr = 4a
⇒ a = πr/2

∴ Area of square = (πr/2)² = π² /4r² = 9.86r²/4 = 2.46r²
and area of circle = πr² = 3.14;r²
and let the side of equilateral triangle is x.
Then, given condition,
3x = 2πr
⇒ x = 2πr/3

∴ Area of equilateral triangle = √3/4 x ²
= √3/4 x 4π²r²/9
= π²/3√3r²
= 1.89r²

Hence, Area of circle > Area of square > Area of equilateral triangle.

Area of equilateral triangle = √3a²/4 = x ......(i)

And perimeter = 3a = y
⇒ a = y/3 ....(ii)

Now, Putting the value of a from Eq. (ii) in Eq. (i). we get
√3 (y/3)²/4 = x

Correct Option: A

Area of equilateral triangle = √3a²/4 = x ......(i)

And perimeter = 3a = y
⇒ a = y/3 ....(ii)

Now, Putting the value of a from Eq. (ii) in Eq. (i). we get
√3 (y/3)²/4 = x
⇒ x = √3 x y²/36
⇒ x = y²/3√3x = y²/12√3
12√3 x = y²
On squaring both sides, we get
y⁴ = 432x²