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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?

Sagot :

Answer:[tex]31.17\ in[/tex]

Step-by-step explanation:

Given

Edge length of cube is [tex]a=18\ in.[/tex]

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

[tex]\Rightarrow (xy)^2+(xz)^2=(yz)^2\\\Rightarrow a^2+(a\sqrt{2})^2=(yz)^2\\\Rightarrow (yz)^2=3a^2\\\Rightarrow (yz)^2=3\times (18)^2\\\Rightarrow yz=18\sqrt{3}\\\Rightarrow yz=31.17\ in.[/tex]

Therefore, the length of the opposite corners is [tex]31.17\ in[/tex]

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