Area–perimeter ratio with side ratio – Find rectangle length:\nThe ratio of area to perimeter of a rectangle is 60:11. Its length : breadth = 6 : 5. Find the rectangle’s length (in units).

Introduction / Context:
Let L = 6x, B = 5x. Then area = 30x^2, perimeter = 22x. The given ratio equates 30x^2 : 22x to 60 : 11 to solve for x.

Given Data / Assumptions:

• L : B = 6 : 5.
• Area : Perimeter = 60 : 11.

Concept / Approach:
30x^2 : 22x = 60 : 11 ⇒ (15x) : 11 = 60 : 11 ⇒ 15x = 60 ⇒ x = 4 ⇒ L = 24.

Step-by-Step Solution:

Final Answer:
24 units