Question

Before 2017, smartphones by major manufacturers all had screens with a aspect ratio. In 2017, two major brands released phones with screens in an aspect ratio. However they still reported their screen size using the same diagonal length of the earlier phones, 5.8 inches. How did the change in aspect ratio affect the screen size, if at all?

Answer 1

the question is missing the numbers, so I looked for a similar one and found that screens back in 2017 had a 16:9 ratio and since then it changed to 18.5:9 ratio

the area of the screen is b x a x 0.5

we can form triangles:

old aspect ratio (16:9):

a = 1.778b

h = √(a² + b²)

5.8 = √[(1.778b)² + b²]

5.8 = √(3.16b² + b²)

5.8² = 4.16b²

33.64 = 4.16b²

b² = 33.64 / 4.16 = 8.0865

b = √8.0865 = 2.8437

a = 2.8437 x 1.778 = 5.056

area = 2.8437 x 5.056 x 0.5 = 7.19 in²

new aspect ratio (18.5:9):

a = 2.0556b

h = √(a² + b²)

5.8 = √[(2.0556b)² + b²]

5.8 = √(4.2253b² + b²)

5.8² = 5.2253b²

33.64 = 5.2253b²

b² = 33.64 / 5.2253 = 6.4379

b = √6.4379 = 2.5373

a = 2.5373 x 2.0556 = 5.2157

area = 2.5373 x 5.2157 x 0.5 = 6.62 in²

the actual screen area decreased by 0.57 in² or 7.93%