The length and breadth of a rectangle are in the ratio 2 : 1. The numerical values of the perimeter and the area of the rectangle are in the ratio 3 : 4. Find the length of the rectangle.

Correct option is D

Given:
- Ratio of length to breadth = 2 : 1
- Ratio of perimeter to area = 3 : 4
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Formula Used:
Perimeter of rectangle = 2 × (Length + Breadth)
Area of rectangle = Length × Breadth
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Solution:
Let the length be 2x and the breadth be x.
Step 1: Perimeter = 2 × (2x + x) = 6x
Step 2: Area = 2x × x = 2x²
Step 3: According to the given condition, the ratio of perimeter to area is 3:4:
(Perimeter) / (Area) = 3/4
=> 6x / 2x² = 3/4
=> 24x = 6x²
=> x = 4
Step 4: Length = 2x = 2 × 4 = 8
Therefore, the length of the rectangle is 8 units.