Question

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

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:
${9}^{2} = {x}^{2} + {5}^{2} \\ {x}^{2} = {9}^{2} - {5}^{2} \\ x= \sqrt{( {9}^{2} - {5}^{2})} = \sqrt{(81 - 25)}$
$x = \sqrt{56} = \sqrt{(8 \times 7)} \\ x= \sqrt{(4 \times 14)} = \sqrt{4}\times \sqrt{14} \\ x = 2 \sqrt{14}$