SOLUTION: A rectangle is inscribed in a semicircle with a diameter of 8 cm. Express the area of the rectangle as a function of he width "w" of the rectangle. I understand I need to find A

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Question 806228: A rectangle is inscribed in a semicircle with a diameter of 8 cm. Express the area of the rectangle as a function of he width "w" of the rectangle.
I understand I need to find A(w) but I have no idea how to find it. Please help!
Answer by solver91311(24713) About Me  (Show Source):
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From the center of the circle construct a radius to one of the vertices of the rectangle that is not on the diameter. This radius will be the hypotenuse of a right triangle that is one-half the length of the rectangle on one leg and the width of the rectangle on the other leg. Since the diameter of the semicircle is 8 cm, the radius is 4 cm.

Using Pythagoras and a little algebra:









which is an expression for the length in terms of the width. Since the area is length times width:



This presumes that the length dimension is the one that is coincident with the semicircle diameter.

John

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