Triangle in a triangle such that one common angle and one similar angle are formed

This question was uploaded on 08/01/22 on social media accounts.

Solution:

Here, one angle is common and one angle is given similar, so both triangles are similar.

One side of both triangles is in the ratio 1:2 and both triangles are similar so all sides are in the ratio of 1:2 and their areas are in the ratio of the square of the ratio of their sides.

Ratio = (1/2)² = 1/4

Ratio = 1:4