Area of sector = ( arc length x radius ) / 2 cm²

Correct Option: C

Area of sector = ( arc length x radius ) / 2 cm²
= (3.5 x 5 ) / 2
= 8.75 cm²

Let length = a metres and breadth = b metres
then, 2(a+b)= 46
⇒ (a+b) =23 and ab =120
∴diogonal = √a²+b²=√(a+b)²-2ab
√23²-2 *120
=√ 289 = 17m

Correct Option: C

Let length = a metres and breadth = b metres
Then, 2(a+b)= 46
⇒ (a+b) =23 and ab =120
∴ Diagonal = √a² + b²
√(23)²-2 x 120
√289 = 17 m

Speed = 12 x (5/18) m/sec
=10/3 m/sec

there4; perimeter = (10/3) x 15 x 60 m=3000 m
∵ 2( a + 4a) = 3000 m
⇒ a = 300 m
So, length = 1200 m and breadth = 300 m

Correct Option: A

Speed = 12 x (5/18) m/sec
=10/3 m/sec

there4; perimeter = (10/3) x 15 x 60 m=3000 m
∵ 2( a + 4a) = 3000 m
⇒ a = 300 m
So, length = 1200 m and breadth = 300 m

∴ Area = (1200 x 300 ) m² = 360000m²

Area of a triangle formed by joining the mid point of the sides of the triangle is 1/4^th of area of the original triangle .

Correct Option: B

Area of a triangle formed by joining the mid point of the sides of the triangle is 1/4^th of area of the original triangle .
So area of Δ DEF = 36/ 4 = 9 m²

Let the longer side = l, shorter side = b and diagonal = d
Then, area of rectangular carpet = l x b = 60 ....(1)

And from question d + l = 5b
⇒ d = 5b - l ...(2)
⇒ d² = 25b² + l² - 10 x lb
⇒ l²+ b² = 25b² + l² - 10 x lb
⇒ l²+b² = 25b² + l² - 10 x 60
⇒ 24b² = 600
∴ b = √25 = 5 m
√ l = 60 / b = 60 / 5 = 12 m

Correct Option: B

Let the longer side = l, shorter side = b and diagonal = d
Then, area of rectangular carpet = l x b = 60 ....(1)

And from question d + l = 5b
⇒ d = 5b - l ...(2)
⇒ d² = 25b² + l² - 10 x lb
⇒ l²+ b² = 25b² + l² - 10 x lb
⇒ l²+b² = 25b² + l² - 10 x 60
⇒ 24b² = 600
∴ b = √25 = 5 m
√ l = 60 / b = 60 / 5 = 12 m