The perimeter of a rectangle is 80 cm. Find the lengths of the sides of the rectangle giving the maximum area. Enter the answers for the lengths of the sides in increasing order.

The lengths of the sides are 20 cm and 20 cm

Step-by-step explanation:

Given

Perimeter, P = 80cm

Represent the length and width with L and W, respectively;

Substitute 80 for P

Divide through by 2

Make L the subject of formula

Area of a rectangle is calculated as thus;

Substitute 40 - B for L

Express this as a function

Set A(B) = 0 to determine the roots

Hence;

or

or

or

The maximum area of a rectangle occurs at half the sum of the roots;

So;

Recall that

Hence the lengths of the sides are 20 cm and 20 cm

a and c

step-by-step explanation: