Find the dimensions and the area of the largest rectangle that can be inscribed

Question

Find the dimensions and the area of the largest rectangle that can be inscribed in the upper half of the ellipse: Numerical Exploration For the default values of a 3 and b 2.5, what approximate value of x gives the largest rectangle area? (Round your answer to two decimal places.) What are the dimensions of this rectangle? (Enter the dimensions as a comma-separated list. Round your answers to two decimal places.) Now try it with a-3, b-4. What approximate value of x gives the largest rectangle area? (Round your answer to two decimal places.) What are the dimensions of this rectangle? (Enter the dimensions as a comma-separated list. Round your answers to two decimal places.) If you change the value of b, does the same value of x give the rectangle with the largest area? O Yes No If you change the value of a, does the same value of x give the rectangle with the largest area? O Yes O No

Explanation / Answer

when a=3,b=2.5

then area of rectangle

x=2.12

dimensions are (4.24,1.77)

Now on changing value of b

a=3,b=4

area of rectangle x=2.12

and dimensions are (4.24,2.83)

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