Sarah asked in Science & MathematicsMathematics · 2 weeks ago

# Find the dimensions of the rectangle?

Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola y=12−x^2. List the dimensions in non-decreasing order.

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• 2 weeks ago

OK so this will involve some calculus.

First, the area of a rectangle is A = b * h, or in this case A = 2x * y where the coordinates on the parabola are (x,y) and (-x,y). The parabola formula is y = 12-x^2, so the area would be equal to A = 2x (12 - x^2) = 24x - 2x^3.

The derivative of this is A' = 24 - 6x^2.

24 = 6x^2.

4 = x^2

x = +/- 2

Plug this back into the equation and you get y = 12 - (+/- 2) ^2 = 8.

The vertices are (-2,0), (2, 0), (-2, 8), and (2, 8). The dimensions (base and height) are 4 and 8, the area is 32.

• 2 weeks ago

So your key words are: rectangle, area, parabola, calculus. Find a search bar and type them in?

• alex
Lv 7
2 weeks ago

Area A= 2x(12-x^2)

dA/dx = 2(12 - 3x^2) = 0 --->x = 2

---> Dimension 4 , 8

• 2 weeks ago

go with jesus my friend.