The sum of the lengths of the edges of a cube is equal to three-fifths of the perimeter of a square. If the numerical value of the volume of the cube is equal to the numerical value of the area of the square, the perimeter of the square is:

Question

Question

This question was previously asked in

RRC Group D Previous Paper 23 (Held On: 19 Sept 2018 Shift 2)

Answer 1

Let, length of edge of a cube = x unit

Length of side of a square = a unit

Number of edges of a cube = 12

According to the question,

⇒ 12x = 4a × 3/5

⇒ a = 5x …… (1)

According to the question,

⇒ x³ = a² …… (2)

From (1) and (2) we get,

⇒ x³ = (5x)²

⇒ x³ = 25x²

⇒ x = 25

∴ Length of side of the square = a = 5 × 25 = 125 units

∴ Perimeter of the square = 4 × 125 = 500 units