Correct Answer - Option 3 : 12.45 cm

Given:

Ratio between perimeter and breadth = 3 : 1

Formula used:

Perimeter of rectangle = 2 × (length + breadth)

Area of rectangle = length × breadth

Calculation:

Let the length and breadth be l and b respectively.

According to question,

2(l + b) : b = 3 : 1

⇒ 2l + 2b = 3b

⇒ b = 2l

Area of rectangle = length × breadth

⇒ 310 = l × 2l

⇒ 310 = 2l^{2}

⇒ l^{2} = 155

⇒ l ≈ 12.45 cm

**∴ The length of the rectangle is nearly 12.45 cm.**