Word Problems

Question

The length of a rectangle is 4 cm more than the width and the perimeter is at least 48 cm. What are the smallest dimensions for the rectangle?

Answer 1

We can represent the information in the word problem as these equations:

 

l = w + 4 cm (the length is 4 cm more than the width)

p ≥ 48 cm (the perimeter is at least 48 cm)

 

We also know that the perimeter of a rectangle can be expressed as:

 

p = l + l + w + w or p = 2(l + w) 

 

To solve for the smallest dimensions, we can set up an equation where width (w) is our only variable (which will later allow us to solve for length). We know that length = w + 4 cm, so we can substitute for length in our equation for perimeter above:

 

p = 2(w + 4 + w) = 2(2w + 4) = 4w + 8

 

Now we can substitute our equation above into the "known" value of p (p ≥ 48 cm), being careful to keep the inequality sign facing the correct way. And solve for width:

 

4w + 8 ≥ 48

4w ≥ 40

w ≥ 10 cm 

 

With this value for width, we can solve for length:

 

l = w + 4 cm

l = (10) + 4

l = 14 cm 

 

The smallest possible dimensions of a rectangle that meet the requirements above are 10 x 14 cm.