Answer:
- side: (12 -a); area: 12a -a²
- n = 1; n = 2
- n = 1; n = 2; n = 3; n = 4
Explanation:
You want the other side length and the area of a rectangle with perimeter 24 and one side 'a'. You want the natural number solutions to ...
- (-27.1 +3n) +(7.1 +5n) < 0
- (2 -2n) -(5n -27) > 0
1. Rectangle
The perimeter is given by the formula ...
P = 2(l +w)
Using the given values, we can find the other sides from ...
24 = 2(a +w)
12 = a +w
w = 12 -a
The area is given by ...
A = lw
A = (a)(12 -a) = 12a -a²
The other side is (12 -a) and the area is A = 12a -a².
2. Negative
Simplifying, we have ...
(-27.1 +3n) +(7.1 +5n) < 0
-20 +8n < 0
8n < 20 . . . . . add 20
n < 2.5 . . . . . . divide by 8
n = 1; n = 2
3. Positive
Simplifying, we have ...
(2 -2n) -(5n -27) > 0
29 -7n > 0
7n < 29 . . . . . . add 7n
n < 4 1/7 . . . . . divide by 7
n = 1; n = 2; n = 3; n = 4
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