How do you find the area of the largest rectangle that can be inscribed in a right traingle with legs of lengths 3 cm and 4cm if two sides of the rectangle lie along the legs?

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Answer 1 · 2015-05-27T00:36:26

Given the diagram below:
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The area of the rectangle is
#A(x) = (3-x)(4/3x)#

#= 4x- 4/3x^2#

The maximum area will occur when the derivative of the Area is equal to zero

#(dA)/(dx) =4 -8/3x = 0#

#4 = 8/3x#

#x = 3/2#

The width of the rectangle will be
#3-x = 3 - 3/2 = 3/2#
The height of the rectangle will be
#4/3 x = 4/3 * 3/2 = 2#

The Area of the rectangle will be
#3/2 * 2 = 3#
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