The ratio of the length to the width to the height of a rectangular prism is 2:1:3 and the sum of the lengths of all its edges is 360 cm. Calculate the height of this rectangular prism.

Answer 1

Here is a sketch:

The height has 4 sides that are "3W" long so that is 12w.

The width has 4 sides that are "w" long so that is 4w.

The length has 4 sides that are "2w" long so that is 8w.

The total is 12w + 4w + 8w and that equals 360 cm

12w + 4w + 8w = 360

24w = 360

w = 15

The height is 3w so 3(15) = 45 cm