A rectangle is constructed with its base on the x-axis and its upper two vertices on the parabola y = 144 - x2. What are the dimensions of the rectangle with the maximum area? What is the area?2.The shorter dimension of the rectangle isand the longer dimension is(Type an exact answer, using radicals as needed.)The area of the rectangle is(Type an exact answer, using radicals as needed.)

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Asked Nov 3, 2019

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A rectangle is constructed with its base on the x-axis and its upper two vertices on the parabola y = 144 - x2. What are the dimensions of the rectangle with the maximum area? What is the area?
2.
The shorter dimension of the rectangle is
and the longer dimension is
(Type an exact answer, using radicals as needed.)
The area of the rectangle is
(Type an exact answer, using radicals as needed.)
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A rectangle is constructed with its base on the x-axis and its upper two vertices on the parabola y = 144 - x2. What are the dimensions of the rectangle with the maximum area? What is the area? 2. The shorter dimension of the rectangle is and the longer dimension is (Type an exact answer, using radicals as needed.) The area of the rectangle is (Type an exact answer, using radicals as needed.)

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check_circleExpert Solution
Step 1

Consider the given parabola.

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Step 2

Let (p, 0) and (-p, 0) be the points on the x-axis.

Therefore, the corresponding points on the parabola will be

(p, 144 – p2) and (-p, 144-p2)

У
(-р, 144-р?),
(р, 144-р?)
(р, 0)
(-р, 0)
X
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У (-р, 144-р?), (р, 144-р?) (р, 0) (-р, 0) X

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Step 3

Formula used:

Area of the rectangl...

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