- #1
nietzsche
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I just can't figure this problem out.
You have four pieces of wood, two with length a and two with length b, and you arrange them in the shape of a kite (pieces of equal length placed adjacent to each other). You want to build a cross in the middle as a support. How long should the middle pieces be to maximize the area of the kite?
Sorry, there was a picture in the textbook, but it should be pretty straight forward.
It's optimization.
I can't figure out how to relate the variables to each other. I know that you can cut the kite in half symmetrically, and rearrange the kite into a rectangle with length y and width x. That was what I tried to do, but I still couldn't figure it out. I ended up with a whole bunch of square roots and I couldn't isolate the variable.
I tried arranging the pieces in different triangles, but I ended up with too many variables.
Any hints would be appreciated.
Homework Statement
You have four pieces of wood, two with length a and two with length b, and you arrange them in the shape of a kite (pieces of equal length placed adjacent to each other). You want to build a cross in the middle as a support. How long should the middle pieces be to maximize the area of the kite?
Sorry, there was a picture in the textbook, but it should be pretty straight forward.
Homework Equations
It's optimization.
The Attempt at a Solution
I can't figure out how to relate the variables to each other. I know that you can cut the kite in half symmetrically, and rearrange the kite into a rectangle with length y and width x. That was what I tried to do, but I still couldn't figure it out. I ended up with a whole bunch of square roots and I couldn't isolate the variable.
I tried arranging the pieces in different triangles, but I ended up with too many variables.
Any hints would be appreciated.