Answer:
The length is 78 feet and the width is 30 feet.
Step-by-step explanation:
The perimeter of a rectangle can be calculated with this formula:
[tex]P=2l+2w[/tex]
Where "l" is the length and "w" is the width.
Since we know that the perimeter of the playing field is 216 feet and its length is 48 feet longer than the width ([tex]l=w+48[/tex]), we can substitute them into the formula and solve for "w":
[tex]216=2(w+48)+2w\\\\216=2w+96+2w\\\\216-96=4w\\\\\frac{120}{4}=w\\\\w=30\ ft[/tex]
Finally, substitute the width into [tex]l=w+48[/tex] to find the length. This is:
[tex]l=30+48\\\\l=78\ ft[/tex]
