Perpendiculars in an isosceles triangle

[Radit2125]

Do you understand the approach I suggested in post 11?

I don't fully understand it. You can see that I found the area of the triangle but I do not know how to continue ( how to set up an equation and solve it for height for each of the small triangles)

 

[lev888]

I don't fully understand it. You can see that I found the area of the triangle but I do not know how to continue ( how to set up an equation and solve it for height for each of the small triangles)

The equation is the area formulas for each of the small triangles. Everything is known there except for the heights.

 

[Radit2125]

But if I don't know the heights of the small triangles, how I would find their areas?
The area of triangle ABC= (AB*QG)/2+ (BC*QF)/2+(QE*AC)/2
12= 4*QG+2,5*QF+2.5*QE

 

[lev888]

But if I don't know the heights of the small triangles, how I would find their areas?
The area of triangle ABC= (AB*QG)/2+ (BC*QF)/2+(QE*AC)/2
12= 4*QG+2,5*QF+2.5*QE

You know the area of ABC. And you know that areas of small triangles are equal.

 

[Radit2125]

Yes, I know this. Could You tell me please, whether I got the right answer?
12= 4*QG+2,5*QF+2.5*QE
2,5*QF= 2.5*QE=> QF= QE
4*QG = 2,5 *QE=> QG= QE*1/1,6
From this we can write:
QE*1/1,6+ 5* QE = 12
QE=32/15= QF
QG= 4/3

 

[lev888]

Yes, I know this. Could You tell me please, whether I got the right answer?
12= 4*QG+2,5*QF+2.5*QE
2,5*QF= 2.5*QE=> QF= QE
4*QG = 2,5 *QE=> QG= QE*1/1,6
From this we can write:
QE*1/1,6+ 5* QE = 12
QE=32/15= QF
QG= 4/3

The second line is not justified. How do you know that 2,5*QF= 2.5*QE from the first line alone?
You should find the area of small triangles first. Then set up 3 separate equations.

 

[Radit2125]

But the small triangles have similar areas. Doesn't that mean that 2,5*QF= 2.5*QE= 4*QG ?
About the second line, I separated the equation.

 

[lev888]

But the small triangles have similar areas. Doesn't that mean that 2,5*QF= 2.5*QE= 4*QG ?
About the second line, I separated the equation.

Yes, they do. But you didn't mention it in your solution.
Try what I suggested - find the small area first and make 3 separate equations.

 

[Radit2125]

But could You tell me how to find the small area if I don't know the heights in the small triangles?

 

[lev888]

But could You tell me how to find the small area if I don't know the heights in the small triangles?

See post 24 and try to figure it out yourself.
The point of the solution is to find the small area and THEN find the heights.

 

[Radit2125]

See post 24 and try to figure it out yourself.
The point of the solution is to find the small area and THEN find the heights.

I understand what You are telling me but I don't know how to do it. I don't know which formula I should use.

 

[lev888]

I understand what You are telling me but I don't know how to do it. I don't know which formula I should use.

There were 12 chocolates. 3 friends ate equal amounts. Have many did each one eat?

 

[Radit2125]

There were 12 chocolates. 3 friends ate equal amounts. Have many did each one eat?

Now I understand. The triangles have areas equal to 4 cm^2. I don’t know how I didnt’t figure it out.? Thank You for the help.
So, the heights (the distance from Q to the sides) of 2 of the triangles are equal to 8/5
and third height is equal to 1. Am I right?