The area of a rectangle is 77m^2 and the length of the rectangle is 10m less than three times the width. What are the dimensions of the rectangle?

Question

The area of a rectangle is 77m^2 and the length of the rectangle is 10m less than three times the width. What are the dimensions of the rectangle?

Answer 1

Shae,

 

You know that the area of a rectangle is length times width.

 

A = l x w

 

We know that l = 3w - 10

We know that A = 77 m²

 

Therefore, 77 = (3w - 10) x w

3w² - 10w = 77

3w² -10w - 77 = 0

 

You need to factor this quadratic equation: (3w + 11) (w - 7) = 0

 

3w + 11 = 0

3w = -11

w = -11/3; width cannot be negative so this is not a solution.

 

w - 7 = 0

w = 7; if width is equal to 7, then the length will be 3w - 10 which is 11.

 

The dimensions of the rectangle are length of 11 and width of 7.

 

If you have questions on factoring, let me know.