Triangulation puzzle

[zenith20]

i have a problem understanding the following puzzle (puzzles 101: Yoshigahara)

Triangulation:
A triangle is divided into four parts by two straight lines as shown. The area ratio of the three parts is 3:7:7
What is the size of the fourth area?

solution:

From
S1S2+7) = 3:7
S2S1+3))=7:7

we get
S1=7.5 & S2=10.5

so
S1+S2=18

could anyone explain the solution to me? thank you in advance

 

[Deleted member 4993]

i have a problem understanding the following puzzle (puzzles 101: Yoshigahara)

Triangulation:
A triangle is divided into four parts by two straight lines as shown. The area ratio of the three parts is 3:7:7
What is the size of the fourth area?

solution:

From
S1S2+7) = 3:7
S2S1+3))=7:7

we get
S1=7.5 & S2=10.5

so
S1+S2=18

could anyone explain the solution to me? thank you in advance

The solution is quite self-explanatory. Exactly where are you stuck?

 

[zenith20]

these parts:

S1S2+7) = 3:7
S2S1+3))=7:7

i could not get 'em

 

[Deleted member 4993]

It is based on the following corollary of properties of triangles:

Triangle ABC is divided into two triangles - ABD and ADC by line AD (D is on BC). Using the formula area of triangle = (1/2)*b*h, you can show that:

(area of ABD)/(area of ADC) = (length of BD)/(length of DC)

Now try it....

 

[mmm4444bot]

To me, this posted puzzle presents an arbitrary triangle with two seemingly arbitrary lines.

I'm certainly puzzled.

Am I supposed to make assumptions about right angles?

 

[Deleted member 4993]

Re:

To me, this posted puzzle presents an arbitrary triangle with two seemingly arbitrary lines.

I'm certainly puzzled.

Am I supposed to make assumptions about right angles?

No - no assumptions necessary. Just name the points of intersections - and use the corollary that I indicated - you'll be there. I don't quite know how to upload a picture (or graph)- and I am not skilled at ASCII drawings (like Soroban) - otherwise I would have posted the solution.

 

[mmm4444bot]

Doh! I drew my first picture wrongly. :roll:

Now the heights cancel.

 

[zenith20]

Thank you dear Subhotosh Khan for your explanation.

 

[Denis]

Thank you dear Subhotosh Khan for your explanation.

dear — adj
4.
a. highly priced
b. charging high prices

How much did he charge you?