the width of a rectangle is 22 centimeters. Find all possible values for the length of the rectangle if the perimeter at least 440 centimetres

Question

i want to know the result of the problem

Answer 1

Good Morning, Liza,

So, you likely know the formula for the perimeter, right? In case you don't; it is as follows: 

P = 2 (L + W)  where P equals the perimeter, L equals the length, and W equals the width, right? Therefore:

P = 2 (L + W) 

But you have a little glitch here, don't you? You are seeking all possible values should the perimeter be at least 440 centimeters, correct? This means that you have an inequality to deal with. No biggie, because you can handle that, right? 

2 (L + W) >= 440       Why? Because we are told the perimeter must be at least 440 centimeters. Notice this equation assures us that we will find all possible values which will satisfy the condition that the perimeter be at least 440 centimeters. Therefore,

2 (L + 22) >=440

L + 22 > = 220     Subtract 22 from both sides of the inequality leaving L to itself. 

L >= 198 centimeters. 


What this is saying, is that if the perimeter is at least 440 centimeters, then the length of your rectangle will be either equal to or greater than 198 centimeters. 


You can proof this answer by plugging the value of 198 into the original perimeter equation. 

I hope I have assisted you and that you have a great upcoming week. If you have further questions, or comments, please feel free to comment below. 

Answer 2

2W + 2L ≥ 440

2(22) + 2L ≥ 440

2L ≥ 396

L ≥ 198 cm

 

The length must be at least 198 cm