Question

Lorena purchased a fish tank in the shape of a cube with sides 18 inches in length. What is the distance between the opposite corners of the front of the tank?

Answer 1

Answer:
`31.17\ in`

Explanation:

Given

Edge length of cube is
`a=18\ in.`

From the figure, distance between the opposite corner of the tank is

`\Rightarrow (xy)^2+(xz)^2=(yz)^2\\\Rightarrow a^2+(a√(2))^2=(yz)^2\\\Rightarrow (yz)^2=3a^2\\\Rightarrow (yz)^2=3* (18)^2\\\Rightarrow yz=18√(3)\\\Rightarrow yz=31.17\ in.`

Therefore, the length of the opposite corners is
`31.17\ in`