Here , we are required to ultimately evaluate the formula to define the perimeter of the window when the length of the base of the window is;
b = 19.
The expression and formula which represents the perimeter of the frame and it's evaluation when b=19 are as follows;
(a) See attached image
(b) The expression is {(π × b)/2} + b
(c) The formular is; P = {(π × b)/2} + b
(d) When b = 19, P = 48.86 inches.
According to the question; the windows are in the shape of a semi-circle with the length of the flat base of the window, b forming the diameter of the circle.
- The Perimeter of a circle is given as;
- p = π × b,
where p = perimeter and b = diameter
Therefore, the perimeter of a semi-circle is;
(π × b)/2
(b) An expression to represent the perimeter or length of the frame of the window (in inches) in terms of the length of the base of the window, b is;
(perimeter of the semi-circle) + length of the base,b
The expression is ; {(π × b)/2} + b
(c) The formular is then given as;
Perimeter, P = {(π × b)/2} + b
(d) To evaluate the formula when b = 19; we have;
P = {(22/7) × (19/2)} + 19
P = 48.86 inches
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