Answer: \(\dfrac{8}{9}\)
Step-by-step explanation:
Formula we use here:
\(\text{Length}=\dfrac{\text{Area}}{\text{width}}\)
Given : Jack lived on a farm and has a large backyard.
The area of the rectangular backyard is \(\dfrac{2}{3}\) of a square mile.
If the width of the yard is \(\dfrac{3}{4}\) of a mile, then the length of width will be :-
\(\text{Length}=\dfrac{\dfrac{2}{3}}{\dfrac{3}{4}}\\\\=\dfrac{2}{3}\times\dfrac{4}{3}=\dfrac{8}{9}\)
Hence, the fraction of a mile is the length of the rectangular backyard= \(\dfrac{8}{9}\)
