im looking at Mechanics of Materials edition 10 specifically

im looking at Mechanics of Materials edition 10, specifically problem 4 ch6 step 11. usually when i use the similar triangle method, i dont consider the entire length of a separate triangle. i usually isolate the triangle im working on and proceed from there. can you explain why they are using the whole length.

Solution

I think what they want is for you to measure on the figure using a ruler (or measure the angles), and figure out the scale factor using your measurement experimentally. Other than that, there is no way you can find the sides without supplementary information. Note that the parallel sides are found also by observation.