Question

geometry find the possible values of x.
the perimeter is less than 28 feet.
7 ft
7 ft
the possible values of x are .

Explanation:

Step1: Calculate the perimeter of the triangle

The perimeter \( P \) of a triangle is the sum of its side lengths. Here, \( P=7 + 7+x=14 + x \).

Step2: Set up the inequality

Since the perimeter is less than 28 feet, we have the inequality \( 14+x<28 \).

Step3: Solve the inequality

Subtract 14 from both sides: \( x<28 - 14 \). So, \( x < 14 \).
Also, by the triangle - inequality theorem, for a triangle with side lengths \( a = 7 \), \( b = 7 \), and \( c=x \), \( x>7 - 7\) (i.e., \(x>0\)).

Answer:

\(0 < x < 14\)