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Freddy has a piece of string that is 20 inches long. He want
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08 Feb 2020, 06:02
08 Feb 2020, 06:02
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Freddy has a piece of string that is 20 inches long. He wants to use the string as the perimeter of a rectangle. What is the greatest area that rectangle could have?
A. 5
B. 10
C. 20
D. 25
E. 40
A. 5
B. 10
C. 20
D. 25
E. 40
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Re: Freddy has a piece of string that is 20 inches long. He want
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09 Feb 2020, 07:42
09 Feb 2020, 07:42
GeminiHeat wrote:
Freddy has a piece of string that is 20 inches long. He wants to use the string as the perimeter of a rectangle. What is the greatest area that rectangle could have?
A. 5
B. 10
C. 20
D. 25
E. 40
A. 5
B. 10
C. 20
D. 25
E. 40
Concept to be used: For a given sum, the product is MAXIMUM when the terms are equal.
Say: a + b = 10
Let us take different combinations:
a = 1, b = 9: a * b = 9
a = 2, b = 8: a * b = 16
...
a = 5, b = 5: a * b = 25
We can use the same concept here:
Assuming the length and width as L and W:
Perimeter = 20 => \(2(L + W) = 20\)
\(=> L + W = 10\)
Thus, \(Area = L * W\) is maximum when \(L = W = 5\)
\(=> Maximum Area = 5 * 5 = 25 \)
Answer D
Re: Freddy has a piece of string that is 20 inches long. He want
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10 Feb 2020, 05:39
10 Feb 2020, 05:39
Here, 20 inch long piece stiring can form different kinds of rectangular. But If the rectangular is squre then it will have greatest area. so if the square is formed by same side 5 iinches, then it's greatest area will be 25.
Ans: 25
Ans: 25
