Question

A rectangular field has an area of 1764 m squared. The width of the field is 13 m more than the length. What is the perimeter of the field?

Answer 1

`\bf \textit{area of a rectangle}\\\\ A=LW~~ \begin{cases} L=length\\ W=width\\ ---------\\ A=1764\\ W=\stackrel{\textit{13 more than L}}{L+13} \end{cases}\implies 1764=LW \\\\\\ 1764=L(L+13)\implies 1764=L^2+13L\implies 0=L^2+13L-1764 \\\\\\ 0=(L+49)(L-36)\implies L= \begin{cases} -49\\ \boxed{36} \end{cases}`

well, since the length can't be a negative value, it can't be -49.

now, you know what the length is, since is just L + 13.

the perimeter is of course length + length + width + width, so that'd give us

36 + 36 + 49 + 49.