Consider a function machine that accepts inputs as ordered pairs. Suppose the components of the ordered pairs are natural numbers and the first component is the length of a rectangle and the second is its width. The machine computes the perimeter $($the distance around a figure$)$ of the rectangle. Thus, for a rectangle whose length, $L,$ is $3$ and whose width, $W,$ is $1,$ the input is $(3,1)$ and the output is $2*3+2*1,$ or $8.$ Complete parts $($a$)$ through $($c$)$ below.

a$.$ For each of the following inputs, find the corresponding output: $(1,10),(5,6),(6,5),(\sqrt[\phantom{2}]{5},\sqrt[\phantom{2}]{5}),(x,a).$

The output for $(1,10)$ is

The output for $(5,6)$ is

The output for $(6,5)$ is

$$

$$

The output for $(\sqrt[\phantom{2}]{5},\sqrt[\phantom{2}]{5})$ is $$

The output for $(x,a)$ is $$