An advertiser rents a rectangular billboard that is 44 ft wide and 20 ft tall. The rent is \( \$ 15 \) per square foot. For a billboard twice as tall, the advertiser has to pay \( \$ 26,400 \). Is this reasonable? Explain. Yes; when the height is doubled, the area is also doubled. No; when the height is doubled, the area is multiplied by \( 1 / 2 \). No; when the height is doubled, the area is multiplied by \( 1 / 4 \). Yes; when the height is doubled, the area is multiplied by 4 .

Let's break this down! The original billboard has an area of \(44 \, \text{ft} \times 20 \, \text{ft} = 880 \, \text{ft}^2\). At \( \$15 \) per square foot, the rent amounts to \( 880 \, \text{ft}^2 \times 15 = \$13,200\). Now, if the height is doubled to \(40 \, \text{ft}\), the new area would be \(44 \, \text{ft} \times 40 \, \text{ft} = 1760 \, \text{ft}^2\). The rent for this would be \(1760 \, \text{ft}^2 \times 15 = \$26,400\). So, yes, this is reasonable as the area indeed doubles with a height increase! In mathematics and real-world applications, understanding dimensions and rates is essential, especially for professionals in real estate and advertising. This concept helps them in making budget decisions that align with trends in space usage. Keep in mind that every additional square foot adds to the overall cost, so calculating areas accurately before signing any contracts can save you from surprises!