Question

the length of a rectangle is 1 yd less than double the width and the area of the rectangle is 21 yd^2, what are the dimensions of the rectangle

Answer 1

So if say the width is "w", double that is 2*w, or 2w 1 unit less than that is 2w - 1, check the picture below

$\bf A=length\cdot width\qquad \begin{cases} length = 2w-1\\ width = w\\ A=21 \end{cases}\implies 21=(2w-1)w \\\\\\ 21=2w^2-w\implies 0=2w^2-1-21 \\\\\\ 0=(2w-7)(w+3)\implies \begin{cases} 0=2w-7\implies &\boxed{\frac{7}{2}=w}\\\\ 0=w+3\implies &-3=w \end{cases}$

since it cannot be a negative value, so... is not -3

what are the dimensions? well, length = 2w - 1, and  w = well is above :)