Question

In an equilateral `Delta ABC, D ` is the midpoint of AB and E is the midpoint of AC. Then, `ar (Delta ABC) : ar (Delta ADE)=?`

A. `2:1`
B. `4:1`
C. `1:2`
D. `1:4`

Answer 1

Correct Answer - B
Clearly, `(AD)/(AB)=(AE)/(AC)=(1)/(2) and angle A= angle A` ( common)
`:. Delta ABC~Delta ADE` [ by SAS-similarity]
`:. Ar(Delta ABC): ar (Delta ADE)=((AB)/(AD))^(2)=((2)/(1))^(2)=(4)/(1)=4:1`