# (Highschool Geometry) Finding side $y$

To find the sum of X, I simply did $\frac{3.4}{4.1} =\frac{ x}{ 6.7}$ and solved for $x$ giving me the correct value of $5.6$cm, however I do not know how to find the value of Y. What property should I be thinking of in problems like these? I mean, is their any relationship, do I have to use pytahgoras theorem or something?

• The tag 'algebraic geometry' is not appropriate ;) – user111187 May 22 '14 at 8:51
• In the little triangle, the shortest side is 3.4, and the longest is $y$. In the big triangle, what's the shortest side? the longest side? Then what do you do? – Gerry Myerson May 22 '14 at 9:53

The two triangles are similar Triangles

similar triangles because line having length "y" is parallel to line having length "18.7 cm" and they have a common angle at top vertex.

The line with length 3.4cm and 4.1cm is a straight line which acts as a transversal cutting those parallel lines which means those parallel lines make the same angle with that line. The same goes to the other line and other two angles are also equal.

Two triangles having same angles but different side lengths are similar . so we can write

3.4/(3.4+4.1) = x/(x+6.7) = y/18.7 = factor

i added to get the total length of the sides of big triangles

• This is wrong. First, the triangles are similar, not congruent. Second, 4.1 is part of a side, whereas most of your other number are all of a side. – Gerry Myerson May 22 '14 at 9:51
• @GerryMyerson-sry for my wrong reply before, thank you – Sudheer May 22 '14 at 12:41