
A rectangle is inscribed in an isosceles

Answer to Problem 91STP
The dimensions of the rectangle when its area is maximum are 5 inches and 4 inches.
Explanation of Solution
Given:
The diagram is :
Concept Used:
- To maximize a function f(x), take its derivative wrt x and equate it to 0:
If
Calculation:
In the given triangle, let
2b = length of the base of the triangle = 10 in.
h = height of the triangle = 8 in.
In the given rectangle , let
2x = length of the base adjacent to the base of the triangle
y = width of the rectangle
The triangles
So,
The area of the rectangle is:
Now, we need to maximize the area of the rectangle . So, we will derivative the function that represents the area of the rectangle wrt x and equate it to 0:
Hence,
The length of the rectangle =
The width of the rectangle =
So, the dimensions of the rectangle when its area is maximum are 5 inches and 4 inches.
Chapter 7 Solutions
Algebra 2
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