Subject: General Aptitude · Chapter: Area · Exam: 2007 · Marks: · Difficulty:
A rectangular carpet has an area of 120 sq. metres and a perimeter of 46 metres. Find the length of its diagonal.
Answer
Answer (as printed):
Explanation
Let the length and breadth of the rectangle be l and b metres respectively. Then, 2 (l + b) = 46 ⇒ l + b = 23 ⇒ b = (23 – l). And, lb = 120 ⇒ l(23 – l) = 120 ⇒ 23l – l2 = 120 ⇒ l2 –23l + 120 = 0 ⇒ l2 – 15l – 8l + 120 = 0 ⇒ l (l –15) – 8 (l – 15) = 0 ⇒ (l – 15) (l – 8) = 0 ⇒ l = 15. So, l = 15 and b = 8. \ Length of diagonal = l 2 + b 2 = (15)2 + 8 2 m = 289 m = 17 m.
Explanation as extracted from the printed page; notation may be imperfect.