Instead of walking along two sides of a rectangular field, Fran took a shortcut along the diagonal. By taking the schortcut, Fran can save a distance equal to half of the length of the longer side. Write an equation that describes this relationship.

(Diagram to come.)

Question

Instead of walking along two sides of a rectangular field, Fran took a shortcut along the diagonal. By taking the schortcut, Fran can save a distance equal to half of the length of the longer side. Write an equation that describes this relationship. 

(Diagram to come.)

anonymous · Answer

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anonymous · Answer

Well you know that hypothenuse = the sum of the two adjacent sides - longer adjacent side/2

anonymous · Answer

However, you can't know if a is longer than b, since that is not given.

anonymous · Answer

The other part of the problem says let a equal the short side and b equal the long side and c, fran's path. Sorry, I forgot to write this. 

So I would just do 1/2b = ?

anonymous · Answer

you know that hypothenuse = the sum of the two adjacent sides - longer adjacent side/2

Put this into a nice equation with variables

anonymous · Answer

And that will be the answer to the question

anonymous · Answer

I don't understand......I know that the hypotenuse = a^2 + b^2

phi · Answer

think like this:  the long way is a+b
the short cut is c
the difference between the long way and the short way is
(a+b)-c
this difference is b/2  (b is the longer side)
so
(a+b)-c = b/2

anonymous · Answer

Yes. But they're not asking about the pythagorean theorem. They just want you to put it into an equation that corresponds to the given information.

anonymous · Answer

Thanks phi and thanks xcrypt!