Re: Julian takes a 10-inch by 10-inch square piece of paper and
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15 Jun 2021, 22:25
In order to compute the perimeter of one of the smaller triangles, first compute the length of the diagonal. For a square with side length 10 inches,
the length of the diagonal can be computed by the Pythagorean theorem,
(diagonal)2 = (side)2 + (side)2:
d2 = 102 + 102
d2 = 200
d = 10sqrt(2)
Alternatively, recognize that the diagonal of a square is always times the
side length times sqrt(2)
The second cut goes from the corner to the midpoint of the diagonal, so that
slice is half as long as the diagonal of the square: = .
Similarly, because the remaining line in each of the smaller triangles is half of
a diagonal, each is of length inches:
Summing the lengths of the sides, the perimeter of the smallest triangle is:
Perimeter = 10 +5sqrt(2) + 5sqrt(2)
Perimeter = 10 + 10sqrt(2)