The length of a rectangle is 6 centimeters more than its width. The area is 216 square centimeters. What are the dimensions?

Question

w=width

l=w+6cm=length 

a=216cm^2

Answer 1

Hi Kassidy.

 

Looks like you have a great start.  Let's take it a bit further.

 

a = 216 cm²

 

Now how do we determine area?

a = l w

 

and we know that l = w+6

so 

a = (w+6)w = 216

w² + 6w = 216

and

w² + 6w - 216 = 0

 

Factor the quadratic

(w+18)(w-12) = 0

w+18 = 0       w-12 = 0

w = -18          w = 12

But a dimension cannot be negative so the width is 12cm

 

And since the length is 6 cm longer than the width

l = 12 + 6 = 18

 

The dimensions are 

l = 18

w = 12