Expert: Paul Klarreich - 8/15/2011

Question
A rectangle is inscribed in a semicircle of radius 10 with the base of the rectangle lying along the bottom of semicircle. Express the area of the rectangle as a function of its width.

Answer
Questioner:roniefel
Country:Surigao del Sur, Philippines
Category:Calculus
Private:Yes  <<<<<<<<<<<<<<<<<<<<<<<< CHANGED.
Subject:functions of CALCULUS

Question:

A rectangle is inscribed in a semicircle of radius 10 with the base of the rectangle lying along the bottom of semicircle. Express the area of the rectangle as a function of its width.
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Put your semicircle on the x-axis with center at (0,0).  Then its equation is

y = sqrt(100 - x^2)

Now take any point on the x-axis from 0 to 10.  The height will be y.

Now express the area as xy and you can then write  x = w/2.  You can finish it up now.