Concept explainers
To find: The length of the side of the square and the radius of the circle.
Answer to Problem 88AYU
Solution:
With a 60 ft long wire it is not possible to make square and a circle with a total area of 100 sq ft.
Explanation of Solution
Given:
• Total length of the wire is 60 feet.
• The wire is cut and one piece bend to a square and another is bend to a circle.
• The total area enclosed by the two pieces is 100 sq feet.
Formula Used:
Calculation:
Let,
be the side of the square
be the radius of the circle
The perimeters and area can be written as the following equations
-----Eq(1)
-----Eq(2)
Substituting in Eq(2)
rewritting the above equation as quadratic equation of
The solution of the quadratic equation is
Real solutions exists if
Here and .
Since, real solution does not exist. Hence it is not possible to make square and a circle with a total area of 100 sq ft, with a wire of 60 ft length.
Chapter 11 Solutions
Precalculus
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