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tatiyna
3 years ago
6

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola

Mathematics
1 answer:
kodGreya [7K]3 years ago
5 0

Answer:

Width =√10 and Height = \frac{10}{4}

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 A =h^{2} [5-h^{2} ]=5h^{2} -h^{4}

For, A to be greatest , \frac{dA}{dh} =0 = 10h-4h^{3}

⇒ h[10-4h^{2} ]=0

⇒ h^{2} =\frac{10}{4} {Since, h≠ 0}

⇒ h = ±\frac{\sqrt{10} }{2}

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

⇒k=5-\frac{10}{4} =\frac{10}{4}

Hence, Width = 2h =√10 and Height = k =\frac{10}{4}. (Answer)

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