11. Analyze and Persevere Yama design rectangular sign for her business, which measures \( 10 \frac{3}{8} \) feet by \( 9 \frac{7}{2} \) feet. She wants to add a neon border around the sign, which costs \( \$ 1 \) per foot. How much \( \mathrm{d}_{\mathrm{o}_{\mathrm{es}}} \) the border cost? Explain.

To find the cost of the neon border, we first need to calculate the perimeter of the rectangular sign. The measurements given are \( 10 \frac{3}{8} \) feet and \( 9 \frac{7}{2} \) feet. Converting these to improper fractions yields \( \frac{83}{8} \) feet and \( \frac{25}{2} \) feet respectively. Now, the perimeter \( P \) can be calculated using the formula \( P = 2 \times (length + width) \). This gives us: \[ P = 2 \times \left(\frac{83}{8} + \frac{100}{8}\right) = 2 \times \left(\frac{183}{8}\right) = \frac{366}{8} = 45.75 \text{ feet} \] At the rate of \( \$1 \) per foot, the cost of the neon border would be \( 45.75 \times 1 = \$45.75 \). --- Understanding the significance of neon signs can be super enlightening! Historically, neon lighting gained popularity in the 1920s, giving businesses a colorful and eye-catching way to advertise and attract customers. The vibrant glow of neon is not just about aesthetics; it's about creating a memorable brand image that stands out, especially at night! Practical tips when designing signage include considering layout and color contrast! Ensure the text is legible from a distance, and choose colors that complement each other. Common mistakes include overcrowding the sign with information or using overly complex fonts that make it hard to read quickly. Simplicity and clarity are key to effective signage!