SOLUTION: The primeter of a rectangle is 30 cm, Find the whole-number dimensions of the rectangle with: (a) the greatest area (b) the least area

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Question 588428: The primeter of a rectangle is 30 cm,
Find the whole-number dimensions of the rectangle with:
(a) the greatest area
(b) the least area
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


If you are allowed to use the fact that the largest area rectangle for a given perimeter is a square with side measure of the perimeter divided by 4, then divide 30 by 4 to get 7.5 and then round up to 8.

If you are required to prove that the largest area is a square then write back and I'll show you a proof.

The smallest would be a 0 by 15 rectangle with an area of zero, but a rectangle with a zero dimension is not a rectangle, it is a line. The restriction to stick with whole numbers means the two short sides must measure 1, leaving 14 for the two long sides. 1 times 14 is 14.

John

My calculator said it, I believe it, that settles it
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Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
The formula for perimeter of a rectangle is

The formula for Area is

----------
given:
cm



Substitute this into


Here's a plot of this equation.
is on the horizontal axis

The value of that gives a maximum
is

The rectangle with maximum area is a
square with sides = 7.5 cm
cm2
The minimum area is 15 cm2
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