# How do you find the length and width of a rectangle whose area is 900 square meters and whose perimeter is a minimum?

Length = Width = 30 meters

By signing up, you agree to our Terms of Service and Privacy Policy

To find the length and width of a rectangle with an area of 900 square meters and a minimum perimeter, you can use calculus.

Let ( l ) be the length and ( w ) be the width of the rectangle.

- Write the formula for the area of a rectangle: ( A = lw ).
- Write the formula for the perimeter of a rectangle: ( P = 2l + 2w ).
- Since ( A = lw = 900 ), express ( l ) in terms of ( w ): ( l = \frac{900}{w} ).
- Substitute ( l ) into the perimeter formula to get it in terms of ( w ): ( P(w) = 2\left(\frac{900}{w}\right) + 2w ).
- Simplify the equation: ( P(w) = \frac{1800}{w} + 2w ).
- To find the minimum perimeter, differentiate ( P(w) ) with respect to ( w ) and set it equal to zero: ( \frac{dP}{dw} = 0 ).
- Solve for ( w ) to find the critical points.
- Determine if the critical points correspond to a minimum perimeter.
- Once you find the value of ( w ), use it to find the corresponding value of ( l ) using the equation ( l = \frac{900}{w} ).
- These values of ( l ) and ( w ) will give you the dimensions of the rectangle with the minimum perimeter.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Use Newton's Method to solve the equation? #lnx+e^x=0#
- Andy is 6 feet tall and is walking away from a street light that is 30 feet above ground at a rate of 2 feet per second. How fast is his shadow increasing in length?
- Find the maximum possible total surface area of a cylinder inscribed in a hemisphere of radius 1?
- How do you minimize and maximize #f(x,y)=x^2+y^(3/2)# constrained to #0<x+3y<2#?
- Use Newton's method to approximate the indicated root of the equation correct to six decimal places?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7