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?


1 Answer 1


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, 2018 at 21:19

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