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24. Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L if one side of the rectangle lies on the base of the triangle.
√(3)/2 L-y
h=√(L^2-(L^2/4))
=√((3L^2)/4)
=(√(3)/2)L
((√(3)/2)L)/(L/2)=((√(3)/2)L-y)/x 
((√(3)L)/2)*(2/L)=((√(3)/2)L-y)/x
Solve for y in terms of x.
√(3)x=(√(3)/2)L-y
√(3)x-(√(3)/2)L=-y
-√(3)x+(√(3)/2)L=-y
y=(√(3)/2)L-√(3)x
y=(√(3)/2)(L-2x)
A(x) = 2xy
=2x(√(3)/2)(L-2x)
=√(3)x(L-2x)
=√(3)xL-2√(3)x^2
Solve:
A`(x)=√(3)L-4√(3)x=0
x=(L/4)
A`(0)>0
A`(L/2)<0
Absolute maximum when x=(L/4)
Absolute maximum when x=L/4 and y=√(3)/2(L-(2L)/4)
=√(