SOLUTION: Please help me solve this word problem: A rectangle has area of 100 square inches, and its length are integers. A.What is the largest perimeter possible? B.What is the small

Question 788254: Please help me solve this word problem:
A rectangle has area of 100 square inches, and its length are integers.
A.What is the largest perimeter possible?
B.What is the smallest perimeter possible?

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The length and width (in inches) are whole numbers that multiply to yield 100.
The possible pairs of numbers (factors) are:
1 and 100,
2 and 50
4 and 25
5 and 20
10 and 10.
There are no other options.
The number 100 is not divisible by 3, or by 6, or by 7, or by 8, or by 9, so neither of those numbers could be the smaller factor, and once you get to 10 times 10, you are done finding the smaller factors.

A rectangle 100 inches long by 1 inch wide would have a perimeter (measured in inches) of
.
That's the largest possible perimeter.

A rectangle 10 inches long by 10 inch wide would be a square. (A square is a special kind of rectangle).
It would have a perimeter (measured in inches) of
.
That's the smallest possible perimeter.

The perimeters (in inches) for the other three options are
, , and

In general, the smalllest perimeter of a rectangle with a certain area happens when that rectangle is a square. Also, conversely, the largest area for a rectangle with a given perimeter happens when the rectangle is a square.
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