A semicircle of radius r=3x is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle.

a. Express the area A of the rectangle as a function of x.

b. Express the perimeter P of the rectangle as a function of x.

a. Since the radius is 3x, the diameter is 6x. Then the length of the rectangle is also 6x. The width is the same as the radius, which is 3x.

Therefore,

Area = (6x)(3x) = 18x^2

so, A(x) = 18x^2

b. Perimeter = 2L + 2W

therefore,

perimeter = 2(6x) + 2(3x) = 12x + 6x = 18x

so, p(x) = 18x

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