A Rectangular Playing Field with a Perimeter Of $120$ Meters Is to Have an Area of at Least

Multiple Choice

A rectangular playing field with a perimeter of $120$ meters is to have an area of at least $495$ square meters. Within what bounds must the length of the field lie?

A) between $30$ and $30 + 9 \sqrt { 5 }$ meters
B) between $30 - 9 \sqrt { 5 }$ and $30 + 9 \sqrt { 5 }$ meters
C) between $28 \frac { 1 } { 2 }$ and $30$ meters
D) between $28 \frac { 1 } { 2 }$ and $30 + 9 \sqrt { 5 }$ meters
E) between $28 \frac { 1 } { 2 }$ and $9$ meters