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Modern smartphones come in various screen sizes and aspect ratios. Let’s compare two popular models:
a) Phone A has a screen ratio of 19.5:9. If the screen is 19.5 units wide, how many units high will it be?
b) Phone B has a more traditional 16:9 ratio. If Phone B’s screen is also 9 units high, how many units wide is it?
c) On a grid that is 24 units wide and 12 units high, draw both phone screens starting from the bottom-left corner. Use a solid line for Phone A and a dashed line for Phone B.
d) If both phones have screens that are 9 units high, how many more square units of area does Phone A’s screen have compared to Phone B’s?
e) Phone A has a resolution of 2688 x 1242 pixels and its screen measures 15.5 cm x 7.2 cm. How many pixels per cm² does this screen have? Round to the nearest whole number.
a) If Phone A’s screen is 19.5 units wide, its height will be 9 units, as given in the ratio 19.5:9.
b) For Phone B with a 16:9 ratio, if the height is 9 units, we’ve multiplied the second number in the ratio by 1. So the width would be 16 × 1 = 16 units.
c) The grid drawing is shown in the accompanying diagram.
d) To calculate the difference in area:
– Phone A area: 19.5 × 9 = 175.5 square units
– Phone B area: 16 × 9 = 144 square units
– Difference: 175.5 – 144 = 31.5 square units
Phone A’s screen has 31.5 more square units of area.
e) To calculate pixels per cm²:
– Total pixels: 2688 × 1242 = 3,338,496 pixels
– Screen area: 15.5 × 7.2 = 111.6 cm²
– Pixels per cm²: 3,338,496 ÷ 111.6 ≈ 29,915 (rounded to nearest whole number)
Therefore, Phone A’s screen has approximately 29,915 pixels per cm².
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