Problema Solution
Instead of walking along two adjacent sides of a rectangular field, one can take a short - cut along the diagonal of the field and save a distance equal to half of the longer side. Find the ratio of the shorter side to the longer side.
Answer provided by our tutors
We know that for any diagonal in this rectangle described that a^2 + b^2 = c^2.
Now, by walking the c^2 path, he saved half the distance of b we will say, and call b the longer side, so we know:
c = a + b - b/2, or c = a + b/2
Now, putting this in to the first equation:
a^2 + b^2 = (a + b/2)^2
Expand:
a^2 + b^2 = a^2 + ab + b^2/4
Cancel:
(3/4)b^2 = ab
Divide by b:
(3/4)b = a
So, the ratio is 3:4.