Question 1109373
The length:width ratio is
{{{80:N}}} or {{{80/N}}} for the field measurements,
and {{{N:5}}} or {{{N/5}}} for the scale drawing.
Because it is a scale drawing, those ratios are the same, so
{{{N/5=80/N}}} .
Solving that equation, we get
{{{N^2=5*80}}}
{{{N^2=400}}}
{{{highlight(N=20)}}} .
So, the field is 20 meters wide,
and the scale drawing is 20 centimeters long.
 
NOTES:
1) The length:width ratios are numbers with no units:
{{{80m/"20 m"=4}}} and {{{20cm/"5 cm"=4}}} .
Unless you convert units, the scale factor is a ratio with units:
{{{80m/"20 cm"=4}}}{{{m:cm}}} or
{{{8000cm/20cm=400:1}}} .
2) The problem could have been solved by equating
"calculated" scale factors for length and width,
{{{80/N}}}{{{m/cm}}} or {{{8000/N}}} for length,
and {{{N/5}}}{{{m/cm}}} or {{{100N/5}}} for width.
That is a different reasoning,
and may be a teacher-preferred way to the solution,
but both reasoning are sound and lead to the same result.
In this case, equations without explanations may not raise teacher's objections.
Using the scale factors with {{{m/cm}}} units,
equating scale factors leads to the same
{{{N/5=80/N}}} equation listed above,
because the same {{{N}}} was given for width of one rectangle
and length of the other one.