This is the accompanying figure

enter image description here

Given three squares as in the figure, where the largest square has area 1, and the area A is known. What is the area B of the smallest square.

Upon lookin at the answer for this excercise, I found the following reasoning as part of the solution:

Let the corner of A divide the sides of the big square in two parts x and 1-x. square B have side-length y. For the corner of B to touch the side of A, we must have y/x + y/(1-x) = 1 (the equation for a line)

I do not understand anything about the part with the line-equation, but this seems like a powerful tool i shall have use of knowing. Could someone please explain this for me?


The figure has a lot of similar right triangles. From their leg proportions, we conclude $$ x:(1-x) = (x-y):y=y:(1-x-y)$$

  • $\begingroup$ Thank you, this is helpful. Could you also please show how this leads to y/x + y/(1-x) = 1 and explain why the makers of the question claim this to be the equation of a line? Is it possible to reach this equation without using triangle similarity. I am led to believe it is since those who made the question didnt go through this step before the conclusion that y/(1.x) + y/x = 1 $\endgroup$ – Ferguson Aug 31 '18 at 21:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.