Q8. - Geometry

Question

Each edge of pyramid V- XYZ is 6 cm. Find the following numerical answers.

$XM=\_\_\_$

Step-by-Step Solution

Answer

The length of XM is$3\sqrt{3}\text{\hspace{0.17em}\hspace{0.17em}unit}$ .

Step 1. Given information.

The given$V-XYZ$ pyramid:

Each edge of pyramid is equal to 6.

Step 2. Determine the value.

The length of XMcan be determined by using Pythagoras Theorem in triangle$XMY$ as:

$\begin{array}{c}X{M}^2+M{Y}^2=X{Y}^2\\ X{M}^2=X{Y}^2-M{Y}^2\\ XM=\sqrt{X{Y}^2-M{Y}^2}\end{array}$

 

Further simplify.

$\begin{array}{c}XM=\sqrt{6^2-3^2}\\ =\sqrt{36-9}\\ =3\sqrt{3}\end{array}$

 

Therefore, the length of XM is equal to unit.$3\sqrt{3}$