Question

pythagorean theorem and its converse
${x}^{2} + {5}^{2} = {15}^{2}$

Answer 1

$x^2+25=225 \\ x^2=200 \\ \sqrt{x^2}= \sqrt{200} \\ x=14.14 \\ or \\ x=10 \sqrt{2}$
If
$c^{2} \ \textless \ a^2+b^2$ the triangle would be acute
If
$c^2=a^2+b^2$ the triangle would be right
If 
$c^2\ \textgreater \ a^2+b^2$ the triangle would be obtuse
Hope this helps!