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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.1. B and C2. C3. B4. A and B |
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Answer» Correct Answer - Option 1 : 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 = √[62 + 82] = 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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