How do you find the dimensions of the rectangle of greatest area whose perimeter is 20 cm?
The area of the rectangle is:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the dimensions of the rectangle of greatest area given a fixed perimeter, you can use the method of calculus optimization. Let ( l ) be the length of the rectangle and ( w ) be the width.
- Write down the formula for the area of the rectangle: ( A = lw ).
- Write down the formula for the perimeter of the rectangle: ( P = 2l + 2w ).
- Use the given perimeter to express one of the variables in terms of the other. Here, we can express ( l ) in terms of ( w ) as ( l = \frac{20}{2} - w = 10 - w ).
- Substitute the expression for ( l ) in the area formula: ( A = (10 - w)w ).
- Expand the equation: ( A = 10w - w^2 ).
- To maximize the area, take the derivative of ( A ) with respect to ( w ) and set it equal to zero: ( \frac{dA}{dw} = 10 - 2w = 0 ).
- Solve for ( w ): ( 10 - 2w = 0 \Rightarrow w = 5 ).
- Substitute the value of ( w ) back into the expression for ( l ): ( l = 10 - 5 = 5 ).
- Therefore, the dimensions of the rectangle of greatest area are ( l = 5 ) cm (length) and ( w = 5 ) cm (width).
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.
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 vertex and axis of symmetry for #y = 4x^2 + 7#?
- How do you solve # 2x^2-3x-14=0# by completing the square?
- A private parking garage charges $100 for the first 3 hours plus $ 35 for each additional hour . How do you find the cost of parking one whole day?
- How do you find the axis of symmetry if only given points (0,2) and (6,2)?
- How do you find the roots, real and imaginary, of #y=2x^2 + 13x + 6+4(x -1)^2 # using the quadratic formula?

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