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).
Aptitude
Area
Difficulty: Medium
Choose an option
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A40 units
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B30 units
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C13 units
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D24 units
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ENone of these
Answer
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