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.
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.
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