Question

Hey Jiskha,

came across this problem in my maths homework and I can't seem to solve it.
Can someone maybe help me out?

A Norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle exactly matches the width of the rectangle. Find the dimensions w * h of the Norman window whose perimeter is 500in. that has maximal area.

Answer in inches:

w=

h=

There is also a picture with it.
i(DOT)imgur(DOT)com/kN8kmbI.png

Thanks for the help!

Answer 1

Maximal area of rectangle is a square.

4w = 500

Solve for w.

Answer 2

Unfortunately it is not that easy. I tried. :D
If you have a chance to look at the picture you will understand. :)
Just replace the "(DOT)" in the link with actual dots ".".

Answer 3

see the related questions below. It does get a bit messy.