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
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