SOLUTION: A window has the shape of a rectangle with a semicircle on the bottom. If the area of the window is 24 square feet, write the perimeter of the window in terms of the radius of the

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Question 983855: A window has the shape of a rectangle with a semicircle on the bottom. If the area of the window is 24 square feet, write the perimeter of the window in terms of the radius of the semicircle, r.
Thank you!!

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A, area of whole figure
p, perimeter
r, radius of connected semicircle, also one of the rectangle part's dimensions
h, height dimension perpendicular to r
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A=24

QUESTION: What is perimeter as a function of r?

A=%281%2F2%29pi%2Ar%5E2%2Bh%2Ar
A=%28pi%2F2%29r%5E2%2Bh%2Ar
Solve this for h.
hr=A-%28pi%2F2%29r%5E2
h=A%2Fr-%28pi%2F2%29r-----this formula for h will be used.

p=2h%2Br%2Bpi%2Ar
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Substitute for h.
p=2%28A%2Fr-%28pi%2F2%29r%29%2Br%2Bpi%2Ar
p=2A%2Fr-pi%2Ar%2Br%2Bpi%2Ar
p=2A%2Fr-pi%2Ar%2Bpi%2Ar%2Br
highlight%28p=2A%2Fr%2Br%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A window has the shape of a rectangle with a semicircle on the bottom. If the area of the window is 24 square feet, write the perimeter of the window in terms of the radius of the semicircle, r.
Thank you!!
Perimeter: highlight_green%28%2848+%2B+pi%2Ar%5E2+%2B+4r%5E2%29%2F%282r%29%29