A rectangle for a pet is 4 ft longer than it is wide. Give the possible values for the width W of the pen if its area must be between 165 and 480 sq ft, inclusively . so what would the widths of the smaller and larger values be?

Question

anonymous · Answer

A rectangle for a pet is 4 ft longer than it is wide

It means that if the width is X the length is X+4

radar · Answer

Solve for area. A= lw.  Solve sides for 165.  Solve for 480.  This will give you the range of the sides.

x(x+4)=165,  or x^2 +4x=165
x^2+4x-165=0  factor (x+15)(x-11)=0. roots are x=-15, x=11
choose x=11, then x+4 =15  the sides are 11 and 15 for the 165 area

radar · Answer

Now solve for the larger area of 480 sq ft
x(x+4)=480
x^2 + 4x=480
x^2+4x-480=0
(x+24)(x-20)=0
x=-24, x=20
choose x=20
x+4=24. sides are 20 and 24 ft.

To express x for the range of area would be 
$$11\le  x \le 20$$

anonymous · Answer

Thank you for explaining that unlike the person whom posted before you!