Question

the length of a picture frame is 6 inches more than the width. for what values of x is the perimeter of the picture frame greater than 152 inches?
for x ■, the perimeter of the picture frame is greater than 152 inches.
(type an integer or a decimal.)
enter your answer in the answer box and then click check answer.

Explanation:

Step1: Define length and width

Let width be \( x \), length be \( x + 6 \).

Step2: Perimeter formula for rectangle

Perimeter \( P = 2(\text{length} + \text{width}) = 2(x + (x + 6)) = 2(2x + 6) = 4x + 12 \).

Step3: Set up inequality

We want \( P > 152 \), so \( 4x + 12 > 152 \).

Step4: Solve inequality

Subtract 12: \( 4x > 152 - 12 = 140 \).
Divide by 4: \( x > \frac{140}{4} = 35 \).

Answer:

\( x > 35 \) (so for \( x \) greater than 35, the perimeter is greater than 152 inches)