# Find the dimensions of the rectangle of maximum area whose perimeter is 16 cm ?

The rectangle of maximum area is a square of side length

Then the perimeter is:

so that:

The area is then:

Find the critical points of the function:

and as:

the critical points is a maximum.

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

Let the length of the rectangle be ( l ) cm and the width be ( w ) cm. Given that the perimeter is 16 cm, we have the equation:

[ 2l + 2w = 16 ]

Solving this equation for ( l ), we get:

[ l = 8 - w ]

The area of the rectangle, ( A ), is given by:

[ A = lw ]

Substituting ( l = 8 - w ) into the area formula, we get:

[ A = (8 - w)w ]

To find the maximum area, we can take the derivative of ( A ) with respect to ( w ), set it equal to zero, and solve for ( w ):

[ \frac{dA}{dw} = 8 - 2w ] [ 8 - 2w = 0 ] [ w = 4 ]

Substituting ( w = 4 ) back into the equation for ( l ), we find:

[ l = 8 - 4 = 4 ]

Therefore, the dimensions of the rectangle of maximum area with a perimeter of 16 cm are ( 4 ) cm by ( 4 ) cm.

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.

- How do you find the integral #int_0^1x^2*e^(x^3)dx# ?
- How do you find the area bounded by #y=x+4# and #y=x^2+2#?
- How do you find the volume of a solid that is enclosed by #y=-x^2+1# and #y=0# revolved about the x-axis?
- How do you find the volume of the solid with base region bounded by the triangle with vertices #(0,0)#, #(1,0)#, and #(0,1)# if cross sections perpendicular to the #x#-axis are squares?
- How do you find the integral #int_1^(3)12(1+5x)^5dx# ?

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