Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
Two perpendicular cross roads of equal width run through the middle of a rectangular field of length 80 m and breadth 60 m. If the area of the cross roads is 675 m2, find the width of the roads.
Answer
Answer (as printed):
Explanation
Let ABCD and EFGH denote the cross roads, each of width x metres. Then, area of the cross-roads = area of rectangle ABCD + area of rectangle EFGH – area of square IJKL = (80x + 60x – x2) = 140x – x2. \ 140x – x2 = 675 ⇒ x2 – 140x + 675 = 0 ⇒ x2 – 135x + 5x – 675 = 0 ⇒ x(x – 135) – 5(x – 135) = 0 ⇒ (x – 135) (x – 5) = 0 ⇒ x = 5. [Q x ≠ 135] So, width of road = 5m.
Explanation as extracted from the printed page; notation may be imperfect.