This is a typical exam problem about area ratio which most students hate. For triangles, area ratios are related to side ratios in 2 situations: similar triangles (area:side^2) and equal height triangle (area:side). In this problem, the 2 lines in the triangle can have their side ratios derived from the given area ratios of equal height triangles on them i.e. 2:4 and 3:4. When X is divided into 2 triangles of unknown areas, using these 2 side ratios to set up 2 simultaneous equations for the 2 unknowns is the obvious way to get the solution as illustrated by your video. Understanding the method is as important as getting the solution because the method can be used repeatedly for similar problems.

X cannot be a fixed value. You can draw many triangles with the areas of its 3 regions being equal to those values. There must be a constraint for the triangle. For instance it must be equilateral or one side is known, etc

@bernadetteluandudi2785

6 ай бұрын

Check again. I found the value. There is only one solution

Thank you for labeling the sides, it is easy to follow!

Replacing 2 by m, 4 by n and 3 by s, where n > sqrt(s * m), we obtain: x = m * s * (s + 2 * n + m)/ (n^2 - s * m) implies A(ABC) = n * (n + s) * (n + m)/ (n^2 - s * m).

تمرين جميل جيد . شرح واضح مرتب . يمكن حل هذا التمرين باستخدام نظرية السلم . شكرا جزيلا لكم والله يحفظكم ويرعاكم ويحميكم جميعا . تحياتنا لكم من غزة فلسطين .

تمرين جميل جيد . رسم واضح مرتب . شرح واضح مرتب . شكرا جزيلا لكم والله يحفظكم ويرعاكم ويحميكم جميعا . تحياتنا لكم من غزة فلسطين . هذه نظرية تسمى نظرية السلم .

Very well done

🙏🙏🙏

Also, x = 7.8.

No way…. I thought it was not a unique triangle.

Kolmiota voidaan muokata. ABC=90 ja EBC=45 astetta. Onnistuu ilman kynää ja paperia.

@bernadetteluandudi2785

6 ай бұрын

You create your own problem. Don't add info, and don't remove either.

1/7+1/6=1/4+1/(9+X)

@joserubenalcarazmorinigo9540

8 ай бұрын

Ladder theorem

You never established that any of the triangles were similar, so all of your assumptions are unfounded.

@bernadetteluandudi2785

6 ай бұрын

He did not say they are similar. The rule he has applied is valid for all triangles.