The area of a rectangle is 66 m2 , and the length of the rectangle is 7 m less than three times the width. Find the dimensions of the rectangle.

Question

The area of a rectangle is
66 m2
, and the length of the rectangle is
7 m
less than three times the width. Find the dimensions of the rectangle.

Answer 1

Paula,

 

The area of a rectangle is given by:

 

A = width * length

 

Let 'l' be the length of the rectangle and 'w' be the width.  We know that the length of the rectangle is 7m less than 3 times the width.  We can write this as:

 

l = 3w - 7

 

Plugging this value of l into the area equation, we get:

 

A = w * (3w - 7)

 

66 = 3w² - 7w

 

Subtracting 66 from both sides:

 

0 = 3w² - 7w - 66

 

Now, we need to factor this quadratic:

 

0 = (3w + 11)(w - 6)

 

This means that either 3w + 11 = 0 or w - 6 = 0. 

 

3w + 11 = 0 => 3w = -11 => w = -11/3 (not possible since the width cannot be negative)

 

w - 6 = 0 => w = 6 (the width is 6m)

 

To find l, we substitute 6 for w in  l = 3w - 7:

 

l = 3(6) - 7 = 18 - 7 = 11m (which is our length)

 

I hope this helps.