Similar triangles problem

[branko917]

I am trying to solve this similar triangles problem but without success so far, i need to get values for x and y.
What is known:
L1+L2=15 meters
triangle angles are the same: alpha=beta
Picture of the triangle is in attachment.
I set up equation for relation between L1 and L2 (in attachment).

Thank in advance.

[Guest]

Okay, angles [tex]\alpha[/tex] and [tex]\beta[/tex] are the same and each triangle has a right angle so corresponding sides are all in the same ratio.

Sides of lengths x and 10- x are opposite those angles so are cooresponding sides.
Sides of lengths y and y- 2 are adjacent to those angle so are corresponding sides.
Sides of lengths L1 and L2 are hypotenuses of the right triangles so are corresponding sides.

[tex]\frac{x}{10- x}= \frac{y}{y- 2}= \frac{L2}{L1}[/tex].

From [tex]\frac{x}{10- x}= \frac{L2}{L1}[/tex], [tex]L1x= L2(10- x)= 10L2- L2x[/tex]
[tex]L1x+ L2x=(L1+ L2)x= 10L2[/tex] so [tex]x= \frac{10L2}{L1+ L2}[/tex],

From [tex]\frac{y}{y- 2}= \frac{L2}{L1}[/tex], [tex]L1y= L2(y- 2)= L2y- 2L2[/tex]
[tex]L1y+ L2y= (L1+ L2)y= 2L2[/tex] so [tex]y= \frac{2L2}{L1+ L2}[/tex].