Lets draw a picture of the rectangle:
From our figure, we can note that triangle ABC is a right triangle, so we can apply Pythagorean theorem, that is
[tex]4^2+x^2=8^2[/tex]which gives
[tex]16+x^2=64[/tex]If we move 16 to the right hand side, we get
[tex]\begin{gathered} x^2=64-16 \\ x^2=48 \end{gathered}[/tex]Then, x is given by
[tex]x=\sqrt[]{48}[/tex]since 48 = 16 x 3, we get
[tex]\begin{gathered} x=\sqrt[]{16\times3} \\ x=\sqrt[]{16}\times\sqrt[]{3} \\ x=4\sqrt[]{3} \end{gathered}[/tex]therefore, the answer is
[tex]x=4\sqrt[]{3}[/tex]which is the measure of the longer side.
