The perimeter of a rectangle is 48 feet Describe the possibl

The perimeter of a rectangle is 48 feet. Describe the possible lengths of a side if the area of the rectangle is not exceed 135 square feet.

(Type your answer in interval notation)

Solution:

Here;

L*W>Area

=>L*W > 135 -----Equation-1

and

2*(L+W)=48

=> L+W=24

=> L=24-w

Putting this in equation-1 :

w(24-w) >135

=> w² - 24w +135 > 0

=> (w-15)(w-9) > 0

=> w>9 and w>15

That means:

When width is 9 then length should be>15
When width is 15 length >9