Length of longest edge of cuboid

Question

A cuboid has faces with areas 48cm^2, 54 cm^2 and 72 cm^2. What is the length of its longest edge?

Answer 1

Make a sketch!

LW=48   HW=54   LH=72

 

W=48/L

 

H*48/L = 54

 

H=72/L

 

48*72/(L²) = 54

 

L=sqrt(48*72/54) = 8

 

Then H = 9 and W = 6, i.e. the longest edge is 9.