Given that, l = 2b [Here l = length and b = breadth]

Decrease in length = Half of the 10 cm = 10/2 = 5 cm
Increase in breadth = Half of the 10 cm = 10/2 = 5 cm
Increase in the area = (70 + 5) = 75 sq cm

According to the question,
(l - 5) (b + 5) = lb + 75

Correct Option: B

Given that, l = 2b [Here l = length and b = breadth]

Decrease in length = Half of the 10 cm = 10/2 = 5 cm
Increase in breadth = Half of the 10 cm = 10/2 = 5 cm
Increase in the area = (70 + 5) = 75 sq cm

According to the question,
(l - 5) (b + 5) = lb + 75
⇒ (2b - 5) (b + 5) = 2b² + 75 [since l = 2b]
⇒ 5b - 25 = 75
⇒ 5b = 100
∴ b = 100/ 5 = 20
∴ l = 2b = 2 x 20 = 40 cm

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

We know that, the radius of a circle inscribed in a equilateral triangle = a/[2√3]
Where, a be the length of the side of an equilateral triangle.

Given that, area of a circle inscribed in an equilateral tringle = 154 cm²
∴ π(a/2√3)² = 154

Correct Option: B

We know that, the radius of a circle inscribed in a equilateral triangle = a/[2√3]
Where, a be the length of the side of an equilateral triangle.

Given that, area of a circle inscribed in an equilateral tringle = 154 cm²
∴ π(a/2√3)² = 154
⇒ (a/2√3)² = 154 x (7/22) = (7)a²
⇒ a = 42√3 cm

Perimeter of an equilateral triangle = 3a
= 3(14√3)
= 42√3 cm

Area of square plate = (Side)²
= (2d)²
= 4d²

Area of circular plate = π (d/2)²
= πd²/4

∵ Number of square plates
= [(4d²)/4] / [(πd²)/4]

Correct Option: C

Area of square plate = (Side)²
= (2d)²
= 4d²

Area of circular plate = π (d/2)²
= πd²/4

∵ Number of square plates
= [(4d²)/4] / [(πd²)/4]
= (4 x 4)/π
≈ 5
Since, nearest integer value is 5.