satisfy that: 
and natural number 
,
Y by Adventure10
Consider an 
triangle. From 
we extend the 
side up to a point 
, such that 
. In the same way we do with the 
side then from point 
we extend it to point 
in such a way that 
. Finally, starting from point 
, we extended the 
side until obtain 
such that 
. Knowing that the area of triangle is 
, which is the area of the triangle 
?
triangle. From 
we extend the 
side up to a point 
, such that 
. In the same way we do with the 
side then from point 
we extend it to point 
in such a way that 
. Finally, starting from point 
, we extended the 
side until obtain 
such that 
. Knowing that the area of triangle is 
, which is the area of the triangle 
?This post has been edited 1 time. Last edited by parmenides51, Jul 23, 2021, 9:21 PM
Reason: title
Reason: title
![[asy]
size(8cm);
pair A = dir(110), B = dir(220), C = dir(320), Q = 2C-B, R = 2A-C, P = 2B-A;
dot("$A$", A, dir(185));
dot("$B$", B, dir(180));
dot("$C$", C, dir(270));
dot("$Q$", Q, dir(280));
dot("$R$", R, dir(95));
dot("$P$", P, dir(265));
draw(A--B--C--cycle);
draw(P--Q--R--cycle, blue);
draw(A--R);
draw(C--Q);
draw(B--P);
draw(B--R, dotted);
draw(A--Q, dotted);
draw(C--P, dotted);
[/asy]](http://latex.artofproblemsolving.com/9/f/a/9fa06ff04f9885143908cf32267553808924dfd4.png)
![$$[ABC] = [ACQ] = [AQR] = [ABR] = [BPR] = [BCP] = [CPQ]$$](http://latex.artofproblemsolving.com/7/7/0/7702f51cead9dd4c6eeddfb7900fa26353e0ac56.png)
from equal base lengths and same heights. Thus, ![$[PQR] = \boxed{7x}$](http://latex.artofproblemsolving.com/8/2/6/826e16b5855e7f1fc7dc328d2c1d59335c5c842e.png)
.
