Answer :
Answer:
[tex]22\ m < x < 74\ m[/tex]
Step-by-step explanation:
Let
x ----> the length for the third side
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) [tex]26+48> x[/tex]
solve for x
[tex]74> x[/tex]
Rewrite
[tex]x < 74\ m[/tex]
2) [tex]26+x>48[/tex]
solve for x
subtract 26 both sides
[tex]x> 22\ m[/tex]
therefore
The range of possible lengths, in meters, for the third side is equal to
[tex]22\ m < x < 74\ m[/tex]
The range of the possible length of the third side of the triangle is 22 to 74 (exclusive)
Assume the lengths of a triangle are x, y and z.
The following are the possible inequalities that relate the side lengths
[tex]x + y > z[/tex]
[tex]y + z > x[/tex]
[tex]x + z > y[/tex]
The unknown side length is x.
So, we have:
[tex]x + 26 > 48[/tex]
[tex]48 + 26 > x[/tex]
[tex]x + 48 > 26[/tex]
Solve for x in the three inequalities
[tex]x + 26 > 48[/tex]
[tex]x > 22[/tex]
[tex]48 + 26 > x[/tex]
[tex]74 > x[/tex]
[tex]x + 48 > 26[/tex]
[tex]x > -22[/tex]
The values of x cannot be negative.
So, we ignore the inequality [tex]x > -22[/tex]
We are left with
[tex]74 > x[/tex] and [tex]x > 22[/tex]
Combine the inequalities
[tex]74 > x > 22[/tex]
Rewrite as:
[tex]22 < x < 74[/tex]
Hence, the range of the possible length is 22 to 74 (exclusive)
Read more about triangle inequalities at:
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