Subject: General Aptitude · Chapter: Area · Exam: 2009 · Marks: · Difficulty:
In a triangle ABC, a line XY is drawn parallel to BC meeting AB in X and AC in Y. The area of the triangle AXY is half of the area of the triangle ABC. XY divides AB in the ratio of
(a)1 : 2
(b)2 : ( 2 − 1)
(c)1 : ( 2 − 1)
(d)2: 3
Answer
Answer (as printed): C
Explanation
Note: The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. Since XY || BC, we have: QUANTITATIVE APTITUDE . ∠AXY = ∠ABC and ∠AYX = ∠ACB. Also, ∠A = ∠A (common) So, DAXY ~ DABC. Let area (DABC) = x sq. units. x ( AB)2 x Then, area (DXY) = sq.units = 2 ( AX )2 ( x / 2 ) AB AX + BX BX ⇒ = 2⇒ = 2 ⇒1+ = 2 AX AX AX BX AX 1 ⇒ = ( 2 − 1) ⇒ = . AX BX ( 2 − 1)
Explanation as extracted from the printed page; notation may be imperfect.