The length of a rectangle is twice its breadth. If its length is decreased by 4 cm and breadth is increased by 4 cm, the area of the rectangle increases by 52 cm². The length of the rectangle (in cm) is:

Given : 

Length of rectangle is twice it's breadth.

Length decreases by 4 cm and breadth increases by 4 cm.

Area of rectangle increases by 52 cm².

Formula used : 

Area of rectangle = Length × Breadth

Calculation : 

According to question,

⇒ L = 2B

⇒ L/B = 2x/1x

Area of rectangle = 2x²

Now,

⇒ (2x - 4) × (x + 4) = 2x² + 52

⇒ 2x² + 8x - 4x -16 = 2x2 + 52

⇒ 4x = 68

⇒ x = 17

Length of rectangle = 2x = 2 × 17 = 34 cm

∴ The correct answer is 34 cm.