Question

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

Answer 1

In triangle ABC,
Since it is an equilateral traingle.
AB =BC = AC
Also in triangle BDE,

BD = DE = BE

Also it is given that,
BD = 2/3 BC

Also we know area of equilateral triangle

area = (root3/4) * a^2

in triangle ABC
Area A1 = root3/4 * BC^2

Also, in triangle BDE,
Area A2 = root3/4 * BD^2

Ratio of the areas

R = A1/A2
R = BC^2/BD^2
Putting the value of BD

R = BC^2/ (2/3BC)^2
R = 9/4
Thus the ratio of the areas of triangle to area of triangle BDE

R = 9:4