1. If the perimeter of the rectangle is 100m, find its dimensions if its area is a maximum.

a. Complete the table below for the possible dimensions of the rectangle and their

corresponding areas. The first column has been completed for you.

b. What is the largest area that you obtained?

c. What are the dimensions of a rectangle with the largest area?

d. The perimeter P of the given rectangle is 100. Make a mathematical statement

for the perimeter of the rectangle.

e. Simplify the obtained equation and solve for the length l of the rectangle in

terms of its width w.

f. Express the area A of a rectangle as a function of width w.

g. What kind of equation is the result?

h. Express the function in standard form. What is the vertex?

i. Graph the data from the table in a showing the relationship between the width

and the area.

j. What have you observed about the vertex of the graph in relation to the

dimensions and the largest area?​