SOLUTION: Is it possible to have a rectangle with a 24 inch perimeter and a 36 square inch area

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Question 705910: Is it possible to have a rectangle with a 24 inch perimeter and a 36 square inch area
Found 2 solutions by jim_thompson5910, mouk:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
yes it is possible

Side length = 6

Perimeter: 6*4 = 24

Area = 6^2 = 36

Specifically, this would be a square with side length of 6 inches

Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
Answer: Yes
Proof:
Let the Let the width and height be denoted by w and h respectively
+perimeter+=+2w%2B2h+=+24+
+w%2Bh+=+12+ Eq (1)

+area+=+wh=36+ Eg (2)

From Eq(1) we get +w+=+12-h+

Substituting into Eq (2) we get:
+wh=36+
+%2812-h%29h=36+
+12h-h%5E2=36+
+h%5E2-12h%2B36=0+
+%28h-6%29%28h-6%29=0+
Giving the solution h=6 (repeated)

And from Eq(1) when h=6 then w=6

so a rectangle of length 6 (ie square) satisfies conditions.

The same process will work for other Numbers