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Allisa [31]
3 years ago
15

Find the dimensions of a rectangle (in m) with area 1,728 m2 whose perimeter is as small as possible. (Enter the dimensions as a

comma separated list.)
Mathematics
1 answer:
lozanna [386]3 years ago
7 0

Given :

Area of rectangle.

To Find :

The dimensions of a rectangle (in m) with area 1,728 m2 whose perimeter is as small as possible.

Solution :

Let, the dimensions of rectangle is x and y.

Area, A = xy.

x = A/y.              ....1)

Perimeter, P = 2( x + y )

Putting value of x in above equation, we get :

P = 2( y + \dfrac{A}{y})

For minimum P,

\dfrac{dP}{dx}=2( 1 - \dfrac{A}{x^2})=0\\\\A = x^2

SO, it is a square.

x=\sqrt{A}\\\\x=\sqrt{1728\ m^2}\\\\x=24\sqrt{3}\ m

Therefore, the dimensions are (24\sqrt{3},24\sqrt{3}).24\sqrt{3}

Hence, this is the required solution.

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