Question

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

Explanation:

Step1: Set up perimeter inequality

The perimeter of the triangle is $7 + 7 + x$, and it is less than 28.
$7 + 7 + x < 28$

Step2: Simplify left side of inequality

Combine the constant terms.
$14 + x < 28$

Step3: Solve for x (perimeter limit)

Subtract 14 from both sides.
$x < 28 - 14$
$x < 14$

Step4: Apply triangle inequality theorem

The sum of any two sides must be greater than the third side: $7 + 7 > x$, $7 + x > 7$.
From $7 + x > 7$: $x > 0$
From $7 + 7 > x$: $x < 14$

Step5: Combine valid ranges

Combine the results from perimeter and triangle rules.
$0 < x < 14$

Answer:

$0 < x < 14$