What is the length of the interior diagonal, d, rounded to the nearest hundredth of a centimeter?

Question

The dimensions of a right rectangular prism are shown in the diagram.

What is the length of the interior diagonal, d, rounded to the nearest hundredth of a centimeter?

Answer 1

rectangular box with sides 10 by 10 by 20 cm

has an interior diagonal length = 10sqr6 = about 24.5 cm

you know it's >20 cm from just sort of visually looking at it, but not that much more than 20 cm

first find the diagonal on the top or bottom which has sides 10 and 20

it's length is sqr(10^2 +20^2) = sqr500 = 10sqr5

then another right triangle has sides 10sqr5 and 10

find the hypotenuse of that right triangle

= sqr(500+100) = sqr600 = 10sqr10 = about 24.5 cm