Answer:
Step-by-step explanation:
Let a is the width of the window and diameter of the semicircle and let h be height of the rectangular portion of the window
:
Perimeter:
2h + a + .5x*pi = 21
2h + 2.57a = 21
2h = 21 - 2.57a
h = (10.5-1.285a)
:
What would be the window with the greatest area;
Area = semicircle + rectangle
Radius = .5a
A = (.5*pi*(.5a)^2) + h*a
Replace h with (10.5-1.285a
A = (1.57*.25a^2) + x(10.5-1.285a)
A = .3927a^2 - 1.285a^2 + 10.5a
A = -.8923a^2 + 10.5a
Find the max area by finding the axis of symmetry; x = -b/(2a)
a = 5.88 meter is the width with the greatest area
:
Find the max area
A = -.8923(5.88^2) + 10.5(5.88)
A = -.8923(5.88^2) + 10.5(5.88)
A = -30.85 + 61.74
A = 30.89 sq/ft is max area
