Solve this multiple-choice question and choose the correct option.

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: L = 6*4 = 24; B = 5*4 = 20.Check: Area = 480; Perimeter = 88 ⇒ 480:88 = 60:11 ✔️ Final Answer:24 units

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

Difficulty: Medium

40 units
30 units
13 units
24 units
None of these

Correct Answer: 24 units

Explanation:

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:

L = 6*4 = 24; B = 5*4 = 20.Check: Area = 480; Perimeter = 88 ⇒ 480:88 = 60:11 ✔️

Final Answer:24 units

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