Question

ABC and BDE are two equilateral triangle such that BD =2/3BC.
find the ratio of the area of triangle ABC and BDE

Answer 1

In triangle ABC,Since it is an equilateral traingle.AB =BC = ACAlso in triangle BDE,BD = DE = BEAlso it is given that,BD = 2/3 BCAlso we know area of equilateral triangle area = (root3/4) * a^2in triangle ABCArea A1 = root3/4 * BC^2Also, in triangle BDE,Area A2 = root3/4 * BD^2Ratio of the areas R = A1/A2R = BC^2/BD^2Putting the value of BDR = BC^2/ (2/3BC)^2R = 9/4Thus the ratio of the areas of triangle to area of triangleBDER = 9:4