Simple Math Question - Can't believe I can't get this

[jonthedit]

So I was doing my basic pre-cal level homework and I bumped into this question.

Easy right?

P = 20 [ft]

C of Cir = 2(pi)(r), areas of cir is = pi(r^2) where r is radius

I know this is easy... yet I can not wrap my head around the question? Maybe it is just my brain being weird and I will get it tomorrow morning.

The problem is I am not sure what to solve for or what to do!

 

[geishroy]

A norman window is one that consists of a rectangle with a curved top to it.
the curved top is actually a semicircle that sits on top of the rectangle.
if the perimeter around the norman window is 20 feet, what radius of the
semicircle will provide the greatest window area?
:
Let H = the height of the rectangular portion of the window
:
Let x = the radius of the semi circle on top
:
Half the circumference = pi*x
:
Width of the window = 2x
:
The perimeter:
2H + 2x + pix = 20
Solve for H
2H = 20 - 2x - pix
H =

:
Area formula: A = (H*2x) + .5pi*x^2
Replace H with

A = 2x(

)+

Cancel the 2
A =

+

​

A =

Leaving us with
A =

.5*pi = 1.57
A =

A =

A quadratic equation, find the vertex for max area; a=-3.57, b=20
x =

x =

x = 2.8 ft radius for max area
:
Check solution by finding the perimeter with this radius
Find 2H
2H = 20 - 2(2.8) - 2.8pi
2H = 5.6 ft
Find perimeter:
2H + 2x + pix = 20
5.6 + 2(2.8) + 2.8*pi =
5.6 + 5.6 + 8.8 = 20
;
note that max area is when the rectangular portion, is a square, 5.6 by 5.6

 

[jonthedit]

-help-

THHANK YOU SO MUCH! This really helped me understand what I was missing!
I can do the rest now!