Delisa is designing a website that will be viewable on both computers and mobile devices, so the website as it is seen on a mobile device is proportional to the website as it is seen on a computer. The diagonal of Delisa's computer monitor is 21 inches, and the diagonal of Delisa's tablet is 9.5 inches.
If an image is 16 centimeters wide on the website when it's displayed on Delisa's computer, how wide should the image be on the tablet? Round to the nearest tenth of a millimeter, if necessary.
To find the width of the image on the tablet, we need to calculate the ratio of the diagonals of the computer monitor and the tablet.
First, we need to find the aspect ratio of the computer monitor:
Let the width of the computer monitor be x inches.
Using the Pythagorean theorem:
x^2 + (x*16/21)^2 = 21^2
x^2 + (16x/21)^2 = 441
x^2 + (256x^2/441) = 441
441x^2 + 256x^2 = 184881
697x^2 = 184881
x^2 = 265
x = √265
x ≈ 16.2 inches
So, the aspect ratio of the computer monitor is about 16.2:21.
Next, we find the aspect ratio of the tablet:
Let the width of the tablet be y inches.
Using the Pythagorean theorem:
y^2 + (y*x/16)^2 = 9.5^2
y^2 + (y*16/21)^2 = 90.25
y^2 + (16y/21)^2 = 90.25
441y^2 + 256y^2 = 19148.25
697y^2 = 19148.25
y^2 = 27.5
y = √27.5
y ≈ 5.3 inches
So, the aspect ratio of the tablet is about 5.3:9.5.
To find the width of the image on the tablet, we use the proportion:
16 cm / 16.2 inches = width on tablet / 5.3 inches
Cross multiply:
width on tablet = (16 cm * 5.3 inches) / 16.2 inches
width on tablet ≈ 5.24 cm
Therefore, the width of the image should be about 5.24 cm on the tablet.