Question

ABC and BDE are two equilateral triangles such that D is the mid-
point of BC. Ratio of the areas of triangles ABC and BDE is:​

Answer 1

Answer:

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