Answer:
[tex]x-1<n<3x+5.[/tex]
Step-by-step explanation:
If a, b and c are the lengths of the triangle's sides, then
[tex]a+b>c,\\ \\a+c>b,\\ \\b+c>a.[/tex]
Since
[tex]a=2x+2,\\ \\b=x+3,\\ \\z=n,[/tex]
then
[tex]2x+2+x+3>n\Rightarrow n<3x+5,\\ \\2x+2+n>x+3\Rightarrow n>1-x,\\ \\x+3+n>2x+2\Rightarrow n>x-1.[/tex]
Thus,
[tex]x-1<n<3x+5.[/tex]
Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is A, 3x + 5 > n > x - 1.
Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
(a+b) > c
(b+c) > a
(c+a) > b
Given the three sides of the triangle 2x + 2 ft, x + 3 ft, and n ft. Now using the triangle inequality theorem we can write,
2x + 2 + x + 3 > n → 3x + 5 > n
2x + 2 + n > x + 3 → n > -x + 1
x + 3 + n > 2x + 2 → n > x - 1
Since x can not be a negative term therefore, we can write,
3x + 5 > n > x - 1
Hence, the correct option is A, 3x + 5 > n > x - 1.
Learn more about Triangle Inequality Theorem:
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