To find: The dimension of a rectangle for which its area is maximum and two of its vertices are on x-axis and two vertices are on
The length of inscribed rectangle is and height is .
The given figure is,
Area of rectangle is,
From Figure (1) length is and width is .
Substitute for and y for w in equation (1)
Vertices of the rectangle are on .
Summarize the information in a table as shown below.
|In Words||In Algebra|
|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 in first quadrant (because area and dimensions of rectangle is non-negative) using graphing calculator as shown below.
Observe from Figure (2) that function attains a maximum value when x is 1.63.
Substitute for x in and solve for y.
The length of rectangle for maximum area is,
Substitute for x in above equation
Thus, the length of inscribed rectangle is and height is .
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