Question

abc and bde are two equalateral triangles such that d is the mid point of bc if bd:dc =2:1 then the ratio of the area of ∆abc to that of ∆bde is​

Answer 1

Answer:

Ratio of the area of ∆ABC and ∆BDE

Explanation:

Given:

• △ABC and △BDE are equilateral
• BD = 1/2 BC as D is the midpoint of BC

Solution:

Since △ABC and △BDE are equilateral

Their sides would be in the same ratio

AB/BE = AC/ED = BC/BD

Hence by SSS similarity,△ABC∼△BDE

And, we know that the ratio of area of triangle is equal to the ratio of the square of corresponding sides.

So, area of △ABC/ area of △BDE = BC²/BD²

$= \frac{bc {}^{2} }{( \frac{bc}{2}) {}^{2} }$

since BD = BC/2

$= \frac{4 {bc}^{2} }{ {bc}^{2} }$

$= \frac{4}{1}$

Hence, area of △ABC /area of △BDE = 1/4

= 4 : 1