Question

Question 8
Tick the correct answer and justify:
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the area of triangles ABC and BDE is

(A) 2 : 1
(B) 1 : 2
(C) 4 : 1
(D) 1 : 4

Answer 1

(C) 4 : 1


Given,
$\Delta ABC$ and $\Delta BDE$ are two equilateral triangles.
D is the mid-point of BC.
$\therefore BD=DC=\frac{1}{2}\times BC$
Let each side of $\Delta ABC$ is 2a.
As,$\Delta ABC\sim \Delta BDE$
$\therefore \frac{area\left(\Delta ABC\right)}{area\left(\Delta BDE\right)}=\frac{A{B}^2}{B{D}^2}=\frac{(2a{)}^2}{(a{)}^2}=\frac{4a^2}{a^2}=\frac{4}{1}=4:1$