Question

Find the length of the missing side.

Answer 1

14.4 inches

Explanation:

Use the Pythagorean theorem:
`a^(2) + b^(2)`

So, this will be:
`8^(2) + 12^(2) = c^(2)`

By simplifying we get:

c =
`√(208)`

The missing side is: 14.4 (rounded to the tenth)

Answer 2

`\displaystyle 4 √(13)in`

Explanation:

we are given a right angle triangle and we want to figure out the missing hypotenuse in order to do so we can consider using Pythagoras theorem given by

`\displaystyle {a}^(2) + {b}^(2) = {c}^(2)`

`\displaystyle \implies{c}^{} = \sqrt{ {a }^(2) + {b}^(2) }`

let a and b be 8 and 12 respectively thus

substitute:

`\displaystyle {c}^{} = \sqrt{ {8 }^(2) + {12}^(2) }`

simplify squares:

`\displaystyle {c}^{} = √( 64 + 14 4)`

simplify addition:

`\displaystyle {c}^{} = √(208)`

by simplifying the redical expression we obtain:

`\displaystyle {c}^{} = 4 √(13)`