Answer: 32 cm
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Work Shown
width/height = 4/3
w/24 = 4/3
3w = 24*4
3w = 96
w = 96/3
w = 32 cm is the width
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Another approach.
The ratio of width to height is 4:3, meaning a screen that has width 4 cm and height 3 cm is possible. Instead, we want the "height 3 cm" to be "height 24 cm". This is a jump of "times 8".
Multiply both parts of that ratio by 8 to get...
4:3
8*4:8*3
32:24
A screen that is 32 cm wide and 24 cm tall will give us a ratio 4:3 when simplifying fully.
The order of the numbers is important. We have the width listed first simply because it was listed first in the phrasing "ratio of width to height".