Problem 7.
Suppose a square is inside a right triangle as shown in the picture. If the square is 1 inch on each side and the hypotenuse is inches long, find the length of the vertical (longer) leg of the triangle.
Solution:

Let x be the distance AF and let Y be the distance BF.
Since they have the same angles, triangles ADC and CEB are similar.
Therefore,



x + y = - 3 is discarded and the only solution that makes sense is
x + y = 5 or y = 5 - x.

Substituting y = 5 - x,


These two numbers are the length of the two legs of triangle ABF.
Since the problem asks for the length of the longer leg, the required leg has a



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