Question

Find the dimensions of the rectangle with largest area that can be inscribed in a semicircle of radius
2 inches.

Answer 1

radius = 2
A= lw = 2xy
cos beta =x/r
sine beta = y/r
2cos beta =x
2sin beta =y

so ...A= 2x(4cosbetasinebeta)
Area equals to 8 time cosine beta time sine beta

so just plug in 15 , 30, 45, 60, 75 degree to the formula...then u noticed that at degree 45 the area is four which is the largest area


after that. u know perimeter is 2x+2y
since area eaquals 2xy then y equals to 4/2x

then plug it in the perimeter equatin then you would get 2x +4/x
d/dy 2x+4/x

then you would get radical 2 for y