AB = 6 cm ; AD = 4 cm and ∠ BAD = 30°
Area of parallelogram ABCD = AB x AD x sin 30°

Correct Option: A

AB = 6 cm ; AD = 4 cm and ∠ BAD = 30°
Area of parallelogram ABCD = AB x AD x sin 30°
= 6 x 4 x sin 30° = 12 cm²

area = √3a²/4
where a = side.

Required perimeter = 3a

Correct Option: A

According to the question,
√3a²/4 = 3√3 [ side = a, and area = √3a²/4]
⇒ a²/4 = 3
⇒ a² = 3 x 4
∴ a = 2√3

∴ Required perimeter = 3a
=3 x 2√3
= 6√3 cm

In a triangle
1. Sum of two sides is always greater than 3rd side
2. Difference of two sides is always less than 3rd side

Correct Option: A

In a triangle
Sum of two sides is always greater than 3rd side
i.e., x < 25 + 15 = 40 .....(i)

Difference of two sides is always less than 3rd side
i.e., 25 - 15 = 10 < x ...(ii)

From Eqs. (i) and (ii) , we get
10 < x < 40

We know that in any triangle
"the sum of two sides is always greater than its third side" and
"the difference of two sides is always less than its third side".
(i) 2 + 3 is not greater than 5
(ii) |5 - 2| not less than 3

Correct Option: B

We know that in any triangle
"the sum of two sides is always greater than its third side" and
"the difference of two sides is always less than its third side".
(i) 2 + 3 is not greater than 5
(ii) |5 - 2| not less than 3

Given ratio = 1/3 : 1/4 : 1/5 = 20 : 15 : 12
Let length of the sides be 20k, 15k and 12k.

Then, according to the question,
20k + 15k + 12k = 94

Correct Option: C

Given ratio = 1/3 : 1/4 : 1/5 = 20 : 15 : 12
Let length of the sides be 20k, 15k and 12k.

Then, according to the question,
20k + 15k + 12k = 94
⇒ 47k = 94
∴ k = 94/47 = 2

Smallest side = 12k = 12 x 2 = 24 cm