Area from perimeter and length — Aptitude Question
Area from perimeter and length: A rectangle has a perimeter of 56 cm and a length of 16 cm. What is its area? Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
A rectangle has a perimeter of 56 cm and a length of 16 cm. What is its area?
Options
- 168 cm²
- 180 cm²
- 192 cm²
- 224 cm²
Show the answer and the worked solution
Correct answer: C. 192 cm²
Worked solution
- l + b = 56/2 = 28, so b = 28 − 16 = 12 cm.
- Area = 16 × 12 = 192 cm².
Answer: 192 cm².
The idea
Halve the perimeter to get l + b, then subtract the known side. Two lines, no equations.
Shortcut. Divide each option by 16: only 192 gives a breadth (12) that fits the perimeter, since 2 × (16 + 12) = 56; 224 gives 14 and a perimeter of 60.
Common trap. 224 cm² — taking the breadth as 56 ÷ 4 = 14, the side of a square with that perimeter; with length 16 the breadth is 28 − 16 = 12.