In Δ ABC, AB = AC and AL is perpendicular to BC at L. In Δ DEF, DE = DF and DM is perpendicular to EF at M. If (area of Δ ABC) : (area of Δ DEF) = 16 : 25, then (DM + AL)/(DM - AL) is equal to:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 9.
Explanation:
(Area of Δ ABC) : (Area of Δ DEF) = 16 : 25
By the property of a similar triangle,
(DM)2/(AL)2 = 25/16
⇒ DM/AL = 5/4
By componendo dividendo:
⇒ (DM + AL)/(DM - AL) = (5 + 4)/(5 - 4)
⇒ (DM + AL)/(DM - AL) = 9/1 = 9