The area of a rectangle is 27 m2 , and the length of the rectangle is 3 m less than double the width. Find the dimensions of the rectangle.

Question

I need the actual length and actual width.

Answer 1

Let L be the length of the rectangle and W the width of the rectangle.

 

Area is L * W = 27

 

Since L = 2W -3, substitute this into the equation for the area.

 

(2W - 3) * W= 2W² - 3W = 27

2W² - 3W - 27 = 0

(2W - 9)(W + 3) = 0

 

The value of W is either 4.5 or -3.  But width must be positive so the only valid value is w = 4.5 m

With this value of W, L = 2W - 3 = 6 m

Answer 2

Hi Aaron

 

Call L the length and W the width of this rectangle. Then, the rectangle's area is:

 

L*W = 27 m²

 

We know that : L = 2*W - 3   (length is 3m less than double the width). Substituting it in the formulae of area:

 

(2*W - 3)*W = 27 m2    

 

2*W² - 3*W = 27

 

2*W² -3*W -27 =0

 

Only one solution is possible: W = 9/2  m (the other solution is negative and not valid)

 

Because  L =2*W - 3       The length is:  L = 2*(9/2) - 3  =  6 m

 

The solution is :  L =6 m and W= 9/2 m