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

Question

Quizplus · Accepted Answer

Let the length be $l$ and the width be $w$. The perimeter is $2l + 2w = 120$, so $l + w = 60$. The area is $lw \geq 495$. Solving the system, we find the bounds for $l$ are between $30 - 9 \sqrt { 5 }$ and $30 + 9 \sqrt { 5 }$.

A Rectangular Playing Field with a Perimeter Of 120120120 Meters Is to Have an Area of at Least

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