Where does 1,4 and 9 come in this question and how are we assuming it is 4 times the triangle and 9 times the triangle. The solution got me more questions than answer.
Let me ask you this: Do all three triangles have the same three angles? If so, what does that make the triangles?
What’s the solution//what problem set is this from?
no it doesn’t
Please give steps on how it came to be
The videos explain a concept but my god the questions are so hard then I am asking why watch the video in the first place.
Actually they do.
All three triangles have the same 3 angles. They are similar triangles.
where does 1,4 and 9 come from?
The angle I marked here let’s call it b. This angle b is common for all three triangles. The triangles already share angle a. So if two angles are same then the third angles must also be same among the three triangles.
Since they share the same 3 angles they are similar triangles. What that means is the sides of the 3 triangles are proportional.
The smallest triangle has a side length x, the largest triangle has side length 3x. Then the base will follow the same ratio. That is the base of the largest triangle will be 3 times the smallest triangle. The height of the largest triangle will be 3 times the smallest triangle.
By the same logic, the medium triangle will have a ratio of 2x when it comes to both base and height.
Now the area of triangle formula is
1/2 × b × h
Now you can figure out where 4 and 9 came from