SOLUTION: A rectangle has a perimeter of 14 feet. Which could not be its area? 3.5 sq ft 6 sq ft 10 sq ft 12 sq ft

Question 226598: A rectangle has a perimeter of 14 feet. Which could not be its area?
3.5 sq ft
6 sq ft
10 sq ft
12 sq ft
Found 3 solutions by RAY100, solver91311, Alan3354:
Answer by RAY100(1637)   (Show Source): You can put this solution on YOUR website!
Perimeter = 2(Length + Width)
.
14 = 2 (L=W),,,,,,,given
.
7 = L + W
.
.
but L*W = Area
.
if A= 6,,,L =6,,,,w=1 works
.
if A= 10,,,,L=5,,,,W=2 works
.
if A= 12,,,,L=4,,,,W=3 works
.
but if A=3.5, no factors equal 7
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Any of the given values could be the area only knowing that the perimeter is 14 feet. The maximum area for a rectangle of a given perimeter is when the rectangle is a square, that is when the measure of one side is one-fourth of the perimeter. In the case of a rectangle with a 14 ft perimeter, that square would measure 3.5 feet on a side. 3.5 squared = 12.25 square feet -- larger than the largest value on your list. The lower limit for the area is zero. No matter how small you make one of the sides, you can always find a smaller value that is not zero. But the smaller you make one side, the smaller, and therefore closer to zero, will be the area. Hence the area of a rectangle with a 14 foot perimeter is in the interval

John

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A rectangle has a perimeter of 14 feet. Which could not be its area?
3.5 sq ft
6 sq ft
10 sq ft
12 sq ft
-------
Perimeter = 2L + 2W = 14
L+W = 7
Area = L*W = W*(7-W)
Choosing small values of W, eg, 0.1 --> A = 0.69 sq feet
The max value is at L = W = 3.5 --> A = 12.25 sq feet
Any value >0 and <=12.25 could be the area.
------------
All the values above could be the area.
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