Norman window w/ 20-ft perimeter; find largest area

[jacquelinestpe]

A Norman Window has the shape of a rectangle beneath a semicircle. your neighbor is designing a new house and would like Norman window with a perimeter of 20ft that will let in most light ( that is, have the largest area possible) What should the height of the rectangle and the radius of the circle be to allow this?

 

[Deleted member 4993]

A Norman Window has the shape of a rectangle beneath a semicircle. your neighbor is designing a new house and would like Norman window with a perimeter of 20ft that will let in most light ( that is, have the largest area possible) What should the height of the rectangle and the radius of the circle be to allow this?

First draw an approximate sketch.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

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[stapel]

A Norman Window has the shape of a rectangle beneath a semicircle. your neighbor is designing a new house and would like Norman window with a perimeter of 20ft that will let in most light ( that is, have the largest area possible) What should the height of the rectangle and the radius of the circle be to allow this?

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

For instance, you started by using what you'd learned back in algebra. You drew the picture. You labelled the height "h" and width "w" of the rectangular part. You noted that the radius r of the semicircle is r = w/2. You recalled the formulas for the perimeters of rectangles and circles. You plugged these formulas, and the given perimeter value, into an equation. You solved this equation for one of the variables in terms of the other. You recalled the formulas for the areas of rectangles and circles. You used this to create a formula for the sum of the rectangle and the semicircle. You differentiated to find the maxmimum. And... then what?

Please be complete. Thank you!