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Which of the following statement(s) given below is / are TRUE? A: Cost of fencing a park in the shape of rhombus at the rate of Rs. 24 / m is Rs. 720 if area of park is 96 cm2 and ratio of diagonals of the park is 3 : 4. B: Length of perpendicular from a vertex of an equilateral triangle to opposite side is 6√3 cm of area of triangle is 36√3 cm2. C: Perimeter of an equilateral triangle of area 49√3 cm2 is 42 cm.

Which of the following statement(s) given below is / are TRUE? A: Cost of fencing a park in the shape of rhombus at the rate of Rs. 24 / m is Rs. 720 if area of park is 96 cm2 and ratio of diagonals of the park is 3 : 4. B: Length of perpendicular from a vertex of an equilateral triangle to opposite side is 6√3 cm of area of triangle is 36√3 cm2. C: Perimeter of an equilateral triangle of area 49√3 cm2 is 42 cm. Correct Answer B and C

GIVEN:

Three statements.

CONCEPT:

Mensuration

FORMULA USED:

Area of rhombus = (D1 × D2) / 2

Area of an equilateral triangle = √3a2 / 4

CALCULATION:

A:

Let diagonals of rhombus are ‘3x’ and ‘4x’ respectively.

Area of rhombus = (3x × 4x) / 2

96 = 6x2

⇒ x = 4

Side of rhombus = √ = 10 m

Perimeter of rhombus = 10 × 4 = 40 cm

Cost of fencing = 40 × 24 = Rs. 960

B:

Let side of triangle = ‘a’

Now,

√3a2 / 4 = 36√3

⇒ a = 12

Let length of perpendicular from a vertex = ‘x’

Now,

36√3 = (1 / 2) × x × 12

⇒ x = 6√3 cm

C:

Let side of triangle = ‘a’

Now,

√3a2 / 4 = 49√3

⇒ a = 14

Perimeter of triangle = 3a

= 42 cm

Hence, only statements B and C are TRUE.

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