The diagonal of the rectangle is 10 and one side is 6.

Using the Pythagorean theorem: $\text{diagonal}^2 = \text{length}^2 + \text{width}^2$

$10^2 = 6^2 + w^2 \Rightarrow 100 = 36 + w^2 \Rightarrow w^2 = 64 \Rightarrow w = 8$

Perimeter $= 2(6 + 8) = 2 \times 14 = 28$.