A window of perimeter 8 m consists of a rectangle surmounted by an equilateral triangle on top.
What will be the dimensions of the rectangular part so that the window allows the most sunlight?
FIRST CORRECT ANSWER TO SHOW WORK GETS 10 PTS.
What will be the dimensions of the rectangular part so that the window allows the most sunlight?
FIRST CORRECT ANSWER TO SHOW WORK GETS 10 PTS.
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Side of triangle = s
length of rectangle = l
width of rectangle = s
3s + 2l = 8
We want to maximize area so that the window gets the most sunlight
Area = s²*√3/(4) + sl = s²*√3/(4) + (8s - 3s²)/2 = A(s)
Find the critical points of A(s) by setting A '(s) = 0.
A '(s) = s√3/(2) + 4 - 3s = 0
s = 4/[3 - √3/2] = 1.874 m
l = (8 - 3(1.874))/2 = 1.188 m
Dimensions of rectangular part: 1.188 m X 1.874 m
length of rectangle = l
width of rectangle = s
3s + 2l = 8
We want to maximize area so that the window gets the most sunlight
Area = s²*√3/(4) + sl = s²*√3/(4) + (8s - 3s²)/2 = A(s)
Find the critical points of A(s) by setting A '(s) = 0.
A '(s) = s√3/(2) + 4 - 3s = 0
s = 4/[3 - √3/2] = 1.874 m
l = (8 - 3(1.874))/2 = 1.188 m
Dimensions of rectangular part: 1.188 m X 1.874 m