dimensions

Question

the length of a rectangle is 4m less than three times the width, the area is 55m^2 what are the dimensions

Answer 1

The area of a rectangle is length * width, or:

 

A = L*W

 

Since the length is 4m less than three times the width, we know that:

 

L = 3W - 4  

 

Substituting L into the top equation, we see that:

 

A = (3W - 4) * W

 

Simplifying, we see that 3W^2 - 4W = 55  or:

 

3W^2 - 4W - 55 = 0

 

Factoring, we see that:

 

(3W + 11)(W - 5) = 0

 

So W equals either -11/3 or 5.  Since a rectangle's width can't be a negative number, W = 5.

 

That means that the length must equal 3*5-4, which is 11.

 

Thus the dimensions are 5m  by 11m.