Answer:
2√5
Step-by-step explanation:
The given pyramid is composed of two right angle triangles. Notice the triangles of the pyramid share a common side. With the help of it, we can figure out x
recall Pythagoras theorem
[tex] {a}^{2} + { b }^{2} = {c}^{2} [/tex]
Case-1: Finding the opposite side
here,
To find:
now plug in the value of a and c in the formula respectively:
[tex] {4}^{2} + { b }^{2} = {10}^{2} \\ \implies {b}^{2} = {10}^{2} - {4}^{2} \\ \implies {b}^{2} = 84 \\ \implies \boxed{ b_{1} = 2\sqrt{21}}[/tex]
Case-2: Finding x
here,
- [tex]b_1 \implies c=2\sqrt{21}[/tex]
- b=8
- a[tex]\implies[/tex] x
Utilizing Pythagoras theorem yields:
[tex] {x}^{2} + { 8}^{2} = {(2\sqrt{21})}^{2} \\ \implies {x}^{2} = {(2\sqrt{21})}^{2} - {8}^{2} \\ \implies {x}^{2} = 20\\ \implies \boxed{ x= 2\sqrt{5}}[/tex]
and we're done!
