What is the length and width?

Question

The dimensions of a rectangle are such that it's length is 9 inches more than it's width. If the length were doubled and if the width were decreased by 4 inches, the area would be increased by 84. What are the length and width?.

 

Can someone explain how to solve this problem 

Answer 1

Hi Noelie,

 

let x = length

 

    x - 9 = width (length is 9 inches more than width)

 

2x = length doubled

 

x - 9 - 4 = width decreased by 4

 

now

 

2x (x -13) = 84 + x(x-9)

 

2x² - 26x = 84 + x² -9x

 

x² -17x -84 = 0

 

factor

 

(x-21)(x+4)=0

 

x-21=0

x=21     length  (other factor gives a negative lenght)

 

x-9 =12  width

 

 

 

 

 

 

Hope this helps