We will use the Pythagorean theorem.
The formula is :
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
a = vertical side
b = horizontal side
c = hypotenuse
[tex]1.) \: {9}^{2} + {12}^{2} = {x}^{2} \\ 81 + 144 = {x}^{2} \\ 225 = {x}^{2} \\ \sqrt{225} = \sqrt{ {x}^{2} } \\ x = \color{red}{ \boxed{15}}[/tex]
[tex]2.) \: {5}^{2} + {5}^{2} = {x}^{2} \\ 25 + 25 = {x}^{2} \\ 50 = {x}^{2} \\ \sqrt{50} = \sqrt{ {x}^{2} } \\ x = \color{red}{ \boxed{ \sqrt{50} }}[/tex]
[tex]3.) \: {x}^{2} + {5}^{2} = {10}^{2} \\ {x}^{2} = {10}^{2} - {5}^{2} \\ {x}^{2} = 100 - 25 \\ {x}^{2} = 75 \\ \sqrt{ {x}^{2} } = \sqrt{75} \\ x = \color{red}{ \boxed{ \sqrt{75} }}[/tex]
[tex]4.) \: {48}^{2} + {20}^{2} = {x}^{2} \\ 2304 + 400 = {x}^{2} \\ 2704 = {x}^{2} \\ \sqrt{2704} = \sqrt{ {x}^{2} } \\ x = \color{red}{ \boxed{52}}[/tex]
[tex]5.) \: {x}^{2} + {x}^{2} = {8}^{2} \\ 2 {x}^{2} = 64 \\ \frac{2 {x}^{2} }{2} = \frac{64}{2} \\ {x}^{2} = 32 \\ \sqrt{ {x}^{2} } = \sqrt{32} \\ x = \color{red}{ \boxed{ \sqrt{32} }}[/tex]
[tex]6.) \: di \: ako \: marunong \: nito \: sorry[/tex]
