Question

The diagram shows a 4cm*4cm*4cm cube. find the length of the diagonal AB

Answer 1

Explanation:

First find BC:

`BC^2=BD^2+DC^2` (Pythagoras Theorem)

`\rightarrow BC^2=4^2+4^2`

`\rightarrow BC^2=32`

`\rightarrow BC=√(32) cm`

Now find AB:

`AB^2=AC^2+BC^2` (Pythagoras Theorem)

`\rightarrow AB^2=4^2+(√(32)) ^2`

`\rightarrow AB^2=16+32`

`\rightarrow AB^2=48`

`\rightarrow AB=√(48)=6.9cm`

Diagonal AB = 6.9cm