The area of ΔABC is 104 cm2. If D is the midpoint of BC and E is the midpoint of AB, then the area (in cm2) of ΔBDE is :
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 26.
In ΔBCA & ΔBDE
∠B = ∠B (common angle)
∠BDE = ∠BCA (Corresponding angle)
So
ΔBCA ~ ΔBDE (A-A)
Now,
ar ΔBCA/ar ΔBDE = (BD/BC)2
⇒ 104/arΔBDE = (2/1)2
⇒ 104/arΔBDE = 4
Hence,
arΔBDE = 26