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the screen size of cell phones like tv is a measure of their diagonal .

the screen size of the two phones is given as 127 mm but their aspect ratio is different



a

find the side length of rectangular cell phone screen with an aspect ratio of 16;9 whose diagonal measure is 127mm


b

find the area of this screen show all of ur working and round ur answer to nearest hundredth


c

repeat these calculations for a cell phone with same diagonal measurement but with an aspect ratio of 18.5:9

d

which phone's screen is larager

Respuesta :

Answer:

A) Length = 110.4 mm and width = 62.1 mm

B) A = 6855.84 mm²

C) length = 114.7 mm

width = 55.8 mm

Area = 6400.26 mm²

D) Screen with aspect ratio of 16:9 is bigger

Step-by-step explanation:

A) We are told that the aspect ratio of the phone screen = 16:9. This means that the ratio of the length to the width of the screen is 16:9.

To find the side length, we will say that;

length = 16x

width = 9x

Thus, since the edges are perpendicular, then we can use pythagoras theorem since we know that the diagonal is 127 mm

Thus;

(16x)² + (9x²)] = 127²

256x² + 81x² = 16129

337x² = 16129

x² = 16129/337

x = √(16129/337)

x = 6.9

Thus;

length = 16x = 16 × 6.9 = 110.4 mm

width = 9x = 9 × 6.9 = 62.1 mm

Length = 110.4 mm and width = 62.1 mm

B) area of screen is;

A = length × width

A = 110.4 × 62.1

A = 6855.84 mm²

C) We are told that the aspect ratio is now 18.5:9.

Thus;

length = 18.5x

width = 9x

Thus;

(18.5x)² + (9x²)] = 127²

342.25x² + 81x² = 16129

423.25x² = 16129

x² = 16129/423.25

x = √(16129/423.25)

x = 6.2

length = 18.5x = 18.5 × 6.2 = 114.7 mm

width = 9x = 9 × 6.2 = 55.8 mm

Area = 114.7 × 55.8 = 6400.26 mm²

D) Screen with aspect ratio of 16:9 is bigger

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