The expression x – 1 < n < 3x + 5 represents the possible values of n, in feet whose side lengths are (2x+2) ft, (x+3) ft, and n ft.
The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
We have a triangle whose side lengths measures are (2x+2) ft, (x+3) ft, and n ft.
If we take the first two sides are (2x+2) ft, (x+3) ft, and third is n ft.
By the triangle property, that sum of the two sides is always greater than the third side.
2x+2+x+3 > n
3x+5 > n  .....(1)
Now take first two sides as n ft, (x+3) ft, and third side (2x+2) ft
n+x+3 > 2x+2
n > x-1 .....(2)
From the inequality (1) and (2), we get:
x – 1 < n < 3x + 5
Thus, the expression x – 1 < n < 3x + 5 represents the possible values of n, in feet whose side lengths are (2x+2) ft, (x+3) ft, and n ft.
Learn more about the triangle here:
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