We can create two equations from the information given.
"The perimeter of a rectangular field is 76 m."
[tex]\sf P=l+w[/tex]
[tex]\sf 76=l+w[/tex]
"The length is 1 m less than double the width."
[tex]\sf l=2w-1[/tex]
Let's plug in this for 'l' in the first equation:
[tex]\sf 76=(2w-1)+w[/tex]
Combine like terms:
[tex]\sf 76=3w-1[/tex]
Add 1 to both sides:
[tex]\sf 77=3w[/tex]
Divide 3 to both sides:
[tex]\sf w=\boxed{\sf\dfrac{77}{3}}[/tex]
Plug this into any equation to find the length:
[tex]\sf 76=l+w[/tex]
[tex]\sf 76=l+\dfrac{77}{3}[/tex]
Subtract 77/3 to both sides:
[tex]\sf \dfrac{228}{3}-\dfrac{77}{3}=l[/tex]
[tex]\sf l=\boxed{\sf\dfrac{151}{3}}[/tex]
So the width is 77/3 and the length is 151/3. Or we can convert them into mixed numbers:
[tex]\sf 25\dfrac{2}{3}[/tex], [tex]\sf 50\dfrac{1}{3}[/tex]
