High-definition (HD) televisions today have a 16 : 9 aspect ratio (width to height). The advertised screen size is equal

to the screen diagonal.

Allowing for 2 inches of Styrofoam padding on all sides of the TV, what is the smallest possible length and width of a

shipping box for a 75-inch HD TV?

A) 60 by 45

B) 68 by 40

C) 64 by 36

D) 75 by 44

B) 68 by 40

Step-by-step explanation:

First we multiply this ratio by any whole number 16 : 9. At least to get close to the option.

So I multiplied by 4

Giving me 64:36

So we remember that there is a padding of on both sides of the length and width.

This padding is 2 inch each

It's going to be

= 64 + (2+2) : 36 + (2+2)

= 68:40

The most correct option is;

B) 68 by 40

Step-by-step explanation:

Here we have that the advertised screen size = Screen diagonal

Size of the HD TV = 75-inch

Therefore, diagonal of HD TV = 75-inch

Where the width of the HD TV = w

The height of the HD TV = h

h² + w² = 75²

w/h = 16/9

w = 16/9*h

∴ h² + (16/9*h) ² = 75²

337/81*h² = 75²

h = 36.8 in.

Therefore, w = 16/9*36.8 = 65.4 in.

Hence when the thickness of the Styrofoam cup is added, we have;

2 inches on both sides gives 4 inches to be added to both height and width

Which gives, height = 36.8 + 4 = 40.8 in.

Width = 65.4 + 4 = 69.4 in.

The smallest possible dimensions is approximately

69.4 in. by 40.8 in.

Hence, the most correct option is B) 68 by 40.