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

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

Area of square = (Side)² = 20²
= 400 sq cm

∴ Area of rectangle
= 1.8 x 400 = 720 sq cm

Let length and breadth of rectangle be 5k and k respectively.
Then, according to the question,
5k x k = 720

Correct Option: B

Area of square = (Side)² = 20²
= 400 sq cm

∴ Area of rectangle
= 1.8 x 400 = 720 sq cm

Let length and breadth of rectangle be 5k and k respectively.
Then, according to the question,
5k x k = 720
⇒ 5k² = 720
⇒ k² = 720/5 = 144
∴ k = √144 = 12 cm

Perimeter of rectangle = 2(5k + k) = 12k
= 12 x12 = 144 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.

Let one diagonal be k.
Then, other diagonal = (60k/100) = 3k/5 cm
Area of rhombus =(1/2) x k x (3k/5) = (3/10)

Correct Option: D

Let one diagonal be k.
Then, other diagonal = (60k/100) = 3k/5 cm
Area of rhombus =(1/2) x k x (3k/5) = (3/10)
= 3/10 (square of longer diagonal)
Hence, area of rhombus is 3/10 times.