Chapter 9.8, Problem 15PSB

To determine

To calculate: The diagonal of a cube.

Answer to Problem 15PSB

The diagonal of a cube is $2\sqrt{3}$ .

Explanation of Solution

Given information:

Side $AB=CB=2$

Formula used:The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Calculation:

  

Draw AC.

SideAC and DC can be calculated by applying Pythagoras Theorem.

In right angle triangle CBA , we get

  $\begin{array}{l}{\left(CB\right)}^2+{\left(AB\right)}^2={\left(AC\right)}^2\\ {\left(2\right)}^2+{\left(2\right)}^2={\left(AC\right)}^2\\ {\left(AC\right)}^2=4+4\\ \therefore AC=\sqrt{8}\\ \therefore AC=2\sqrt{2}\end{array}$

Draw DC .

In right angle triangle DAC , we get

  $\begin{array}{l}{\left(DA\right)}^2+{\left(AC\right)}^2={\left(DC\right)}^2\\ {\left(2\right)}^2+{\left(2\sqrt{2}\right)}^2={\left(DC\right)}^2\\ {\left(DC\right)}^2=4+8\\ \therefore DC=\sqrt{12}\\ \therefore DC=2\sqrt{3}\end{array}$