Area from a ratio and perimeter — Aptitude Question
Area from a ratio and perimeter: The length and breadth of a rectangle are in the ratio 3 : 2 and its perimeter is… Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
The length and breadth of a rectangle are in the ratio 3 : 2 and its perimeter is 80 cm. What is its area?
Options
- 336 cm²
- 364 cm²
- 384 cm²
- 400 cm²
Show the answer and the worked solution
Correct answer: C. 384 cm²
Worked solution
- l + b = 80 ÷ 2 = 40.
- Splitting 40 in the ratio 3 : 2 gives l = 24, b = 16.
- Area = 24 × 16 = 384 cm².
Answer: 384 cm².
The idea
Halve the perimeter first — that single step converts a perimeter question into a simple sharing problem.
Shortcut. Sides 3k and 2k give 5k = 40, so k = 8 and the area is 6k² = 6 × 64 = 384.
Common trap. 400 cm² — splitting the half-perimeter 40 equally into a 20 × 20 square, ignoring the 3 : 2 ratio.