Question

ABC and BDE are two equilateral Triangles such that D is the midpoint of BC. Ratio of the areas of triangle ABC and triangle BDE will be:

Answer 1

Answer:

ΔBDE:ΔABC

1:4

Step-by-step explanation:

2BD=BC[D is the mid point of BC]

BE=BD=DE - 1 [ΔBDE is an equilateral triangle]

BC=AB=AC -2 [ ΔABC is an equilateral triangle]

In triangle ABC and triangle BDE

THEREFORE

BD/BC=BE/AB=DE/AC

By SSS Similarity

ΔBDE ≈ ΔABC

NOW

ar(ΔBDE)/ar(ΔABC)=$(BD/BC)^{2}$  [Because ratio of areas of similar

                                                               triangles is equal to the square of the                                        

                                                               ratios of their corresponding sides]

THEREFORE

ar(ΔBDE):ar(ΔABC)=$(BD/BC)^{2}$

                              =$(BD/2BD)^{2}$

                              =$(1/2)^{2}$

                              =1/4 i.e 1:4

Answer 2

Here is your answer user.