 Hello friends, let's work out the following problem and in this problem. We have to pick the correct answer and justify it and it says ABC and VDE are two equilateral triangles such that D is the midpoint of BC ratio of the area of the triangles ABC and VDE is Option A is 2 is to 1, option B is 1 is to 2, option C is 4 is to 1, option D is 1 is to 4. So, let us now move on to the solution. Now we are given that Triangle ABC and VDE are equilateral triangles. So since Triangle ABC and VDE are equilateral they are equi-angular that is they have Equal angles and we know that in Equilateral triangles all the angles are of 60 degrees so in triangle ABC and in triangle BDE each angle is of 60 degrees and hence they are equi-angular and hence Triangle ABC is similar to triangle BDE by angle angle angle similarity criteria. Now we know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides so we have area of triangle ABC upon area of triangle VDE is equal to the square of ratio of their corresponding sides that is BC square upon VD square Now D is the midpoint of BC. So we have area of triangle ABC upon area of triangle VDE is equal to BC square. Now BC is double of BD. D is midpoint of BC. So BC is double of VD or we can say that VD is half of BC. So we have area of triangle ABC upon area of triangle BDE is equal to 4 by 1 So the ratio is 4 is to 1 Hence the correct option is option C. So this completes the question and the session. Bye for now. Take care. Have a good day