Question

The rectangular pupil of an octopus is estimated to be $20$ millimetres long with an area of $(20x-200)$square millimetres. Write an expression that represents the perimeter (in millimetres) of the octopus pupil.

Answer 1

Step 1: Find the width of the pupil

The length of an octopus pupil = $20$ millimetres
Area of an octopus $=(20x-200)$ square. millimetres
We will now factor out $20$ from $(20x-200)$

$$\begin{gathered} \Rightarrow 20\left(x\right)-20\left(10\right) \\ \Rightarrow 20(x-10) \end{gathered}$$

So, the width of the octopus pupil $=x-10$ millimetres

Step 2: Find the perimeter of the pupil

As we know the perimeter of octopus pupil = $2$ (length $+$ width)

$$\begin{gathered} \Rightarrow 2[20+(x-10\left)\right] \\ \Rightarrow 2(20+x-10) \end{gathered}$$

$\Rightarrow 2(x+10)$ millimetres

Hence, perimeter of the octopus pupil is $2(x+10)$ millimetres.