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 = 2l2
⇒ l2 = 155
⇒ l ≈ 12.45 cm
∴ The length of the rectangle is nearly 12.45 cm.