Question

the length of a rectangle is 6 units shorter than 1/4 of the width x. Write an expression for the perimeter of the rectangle.

Answer 1

$\bf \textit{perimeter of a rectangle}\\\\ P=2l+2w\quad \begin{cases} l=length\\ w=width\\ -----\\ l=\frac{1}{4}w-6 \end{cases}\implies P=2\left( \frac{1}{4}w-6 \right)+2w \\\\\\ P=\cfrac{1}{2}w-12+2w\implies P=\cfrac{w}{2}-12+2w\implies P=\cfrac{w-24+4w}{2} \\\\\\ P=\cfrac{5w-24}{2}\implies P=\cfrac{5}{2}w-12$

Answer 2

L=x/4 -6

Perimeter= Length x Width
Width=x
Length= x/4 -6

P=LxW
P=(x/4-6)x(x)