Question

The triangle shown is a right triangle. Create the equation to be used to find the missing lengths.

9_ = _____________________

Answer 1

the equation used to find the missing lengths:
9 = __SR (5^2 + x^2)__
As long as it is a right triangle, this is called the Pythagorean Theorem

`{9}^(2) = {x}^(2) + {5}^(2) \\ \sqrt{ {9}^(2) } = \sqrt{( {x}^(2) + {5}^(2) )} \\ 9= \sqrt{( {x}^(2) + {5}^(2) )}`


** FYI- if you wanted to SOLVE FOR THE MISSING SIDE X, then just switch around the original equation solving in terms of x:

`{9}^(2) = {x}^(2) + {5}^(2) \\ {x}^(2) = {9}^(2) - {5}^(2) \\ x= \sqrt{( {9}^(2) - {5}^(2))} = √((81 - 25)) \\`

`x = √(56) = √((8 * 7)) \\ x= √((4 * 14)) = √(4)* √(14) \\ x = 2 √(14)`