Chapter 9.8, Problem 16PSB

To determine

To calculate:Thediagonal of a cube.

Answer to Problem 16PSB

The diagonal of a cube is $5\sqrt{3}$ .

Explanation of Solution

Given information:

Perimeter of the face $=20$

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:

  

Sides x and d can be calculated by applying Pythagoras Theorem.

If P=20, edge is equal to 5.

  $\begin{array}{l}{\left(5\right)}^2+{\left(5\right)}^2={\left(x\right)}^2\\ 25+25={\left(x\right)}^2\\ {\left(x\right)}^2=50\\ \therefore x=\sqrt{50}\\ \therefore x=5\sqrt{2}\end{array}$

  $\begin{array}{l}{\left(d\right)}^2={\left(5\right)}^2+{\left(5\sqrt{2}\right)}^2\\ {\left(d\right)}^2=25+50\\ \therefore d=\sqrt{75}\\ \therefore d=5\sqrt{3}\end{array}$