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

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

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

Given that, perimeter = 90 cm
⇒ 3a = 90 cm       [a = side]
∴ a = 90/3 = 30 cm
∴ Area = √3a² / 4 = √3/4 x (30)²

Correct Option: A

Given that, perimeter = 90 cm
⇒ 3a = 90 cm       [a = side]
∴ a = 90/3 = 30 cm
∴ Area = √3a² / 4 = √3/4 x (30)²
= 900 x √3/4 = 225√3 sq cm

According to the question,
area = √3a²/4

Correct Option: A

According to the question,
area = √3a²/4
= √243 /4
⇒ a² = √81 x 3/√3
∴ a = √9
= 3 cm