Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If each side of a rhombus is 20 metres and its shorter diagonal is three-fourths of its longer diagonal, then the area of this rhombus must be
(a)375 sq. m
(b)380 sq. m
(c)384 sq. m
(d)395 sq. m
Answer
Answer (as printed): C
Explanation
Let AC = x. Then, BD = x. 4 D C O A B 1 x 1 3 So, OA = AC = and OB = BD = x. 2 2 2 8 2 2 2 x 3x AB = ( OA ) + (OB)2 = + 2 8 x 2 9x 2 25 x 2 5 x 5 x 20 × 8 = + = = . = 20 ⇒ x = = 32 m. 4 64 64 8 8 5 So, the length of diagonals are 32 m and 24 m. 1 2 2 \ Area of the rhombus = × 32 × 24 m = 384 m . 2 80 4d
Explanation as extracted from the printed page; notation may be imperfect.