Arectangle is inscribed with its base on the x-axis and its upper corners on the parabola
y=5−x^2. what are the dimensions of such a rectangle with the greatest possible area?

width =

height =

Width =√10 and Height =

Step-by-step explanation:

Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1) are (h,k) and (-h,k).

Hence, the area of the rectangle will be (h + h) × k

Therefore, A = h²k ..... (2).

Now, from equation (1) we can write k = 5 - h² ....... (3)

So, from equation (2), we can write

For, A to be greatest ,

⇒

⇒ {Since, h≠ 0}

⇒ h = ±

Therefore, from equation (3), k = 5 - h²

⇒

Hence, Width = 2h =√10 and Height = k =. (Answer)