Chapter 9.8, Problem 17PSB

To determine

To calculate: Thealtitude PYof a square pyramid.

Answer to Problem 17PSB

The altitude PY of a square pyramid is $4$ .

Explanation of Solution

Given information:

Perimeter of the base $=24$

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:

  

If P =24,each base edge is equal to 6.

  $YR=\frac{1}{2}ID=3$

Side PY can be calculated by applying Pythagoras Theorem.

In right angle triangle PYR , we get

  $\begin{array}{l}{\left(PR\right)}^2={\left(YR\right)}^2+{\left(PY\right)}^2\\ {\left(5\right)}^2={\left(3\right)}^2+{\left(PY\right)}^2\\ \therefore 25=9+{\left(PY\right)}^2\\ \therefore PY=4\end{array}$