To find: The function that models area of a rectangle with height inscribed in a semicircle of radius 10.
The model that function area of rectangle in terms of its height is .
The given figure is,
Here is rectangle with height and is centre of semicircle with radius 10.
Join the points and in the given Figure (1) with a line to form a triangle as shown in Figure (2) below.
In triangle , is , is radius of semicircle i.e. 10 units.
Apply Pythagorean theorem in triangle and calculate x in terms of h.
Substitute 10 for , x for and h for in above equation.
Add to both the sides of above equation.
Take square root of above equation.
The formula to calculate area of rectangle is,
Substitute for length and h for width in above equation.
Substitute for x in above equation.
The model that function area of rectangle in terms of its height is here h varies between .
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