To find: The dimension of a rectangle for which its area is maximum and two of its vertices are on xaxis and two vertices are on
The length of inscribed rectangle is
Given:
The given figure is,
Figure (1)
Calculation:
Area of rectangle is,
From Figure (1) length is
Substitute
Vertices of the rectangle are on
Summarize the information in a table as shown below.
In Words  In Algebra 
Area 

Length of side rectangle. 

Height of the rectangle 

Use the information in the table and model the area in terms of
The function that models the area of given rectangle is,
Sketch the graph of
Figure (2)
Observe from Figure (2) that function attains a maximum value when x is 1.63.
Substitute
The length of rectangle for maximum area is,
Substitute
Thus, the length of inscribed rectangle is