A TV screen is 1.25 m wide by 70 cm high. The best scale to compare the width to the height would be:
a) 1:1.8
b) 2:1
c) 1.8:1
d) 1:2
Answer (2)
Convert the width to centimeters: 1.25 m = 125 cm.
Calculate the ratio of width to height: 70 125 .
Simplify the ratio: 70 125 = 14 25 ≈ 1.7857 .
Approximate the ratio to the closest option: 1.8:1. The final answer is 1.8 : 1 .
Explanation
Convert to same units First, we need to make sure both measurements are in the same units. The width is given in meters (m) and the height in centimeters (cm). Let's convert the width to centimeters. Since 1 meter is equal to 100 centimeters, 1.25 meters is equal to 1.25 * 100 = 125 centimeters.
Calculate the ratio Now we have the width as 125 cm and the height as 70 cm. To find the ratio of width to height, we divide the width by the height: h e i g h t w i d t h = 70 125
Simplify the ratio To simplify the ratio, we can divide both numbers by their greatest common divisor (GCD). The GCD of 125 and 70 is 5. So, we divide both by 5: 70 ÷ 5 125 ÷ 5 = 14 25
Express in x:1 form Now we want to express this ratio in the form x:1. To do this, we divide both parts of the ratio by 14: 14 25 : 14 14 = 14 25 : 1 Now, let's calculate the decimal value of 14 25 :
14 25 ≈ 1.7857
Compare to options So the ratio is approximately 1.7857:1. We need to find the closest match among the given options: a) 1:1.8 b) 2:1 c) 1.8:1 d) 1:2
Comparing 1.7857:1 to the options, 1.8:1 is the closest.
Final Answer Therefore, the best scale to compare the width to the height is approximately 1.8:1.
Examples
When designing a rectangular advertisement banner, the ratio of width to height is crucial for visual appeal. If you want the banner to be 3 meters wide and 1.5 meters high, the width-to-height ratio is 3:1.5, which simplifies to 2:1. This ratio helps ensure the banner looks balanced and attractive to viewers, whether it's displayed online or in a physical location.
The best scale to compare the width of the TV screen to its height is approximately 1.8:1, making option (c) the correct choice. This is derived by converting the width to centimeters and simplifying the ratio of width to height. Finally, we found that 1.7857 is closest to 1.8:1.
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