Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
Nine playing cards are set up to form a rectangle as shown in the adjoining figure. If the area of the rectangle so formed is 180 square inches, what is its perimeter?
(a)48 inches
(b)56 inches
(c)58 inches
(d)60 inches
Answer
Answer (as printed): C
Explanation
Let the length and breadth of each card be l and b inches respectively. Then, area of each card = (lb) sq.inches Area of the rectangle = Sum of areas of 9 cards = (9 lb) sq. inches. So, 9 lb = 180 ⇒ lb = 20 ...(i) Length of rectangle = (5b) inches. Breadth of rectangle = (l + b) inches. Area of rectangle = 5b(l + b) sq. inches \ 5b(l + b) = 180 ⇒ lb + b2 = 36 ⇒ b2 = 36 – 20 = 16 ⇒ b = 4. Putting b = 4 in (i), we get: l = 5. So, length of rectangle = (5 × 4) inches = 20 inches. Breadth of rectangle = (5 + 4) inches = 9 inches. Perimeter of rectangle = 2(20 + 9) inches = 58 inches.
Explanation as extracted from the printed page; notation may be imperfect.