Find the dimensions of the original rectangle. Use quadratic formula

Question

The length of a rectangle is 7 units more than its width. If the width is doubled and the length is increased by 2, the area is increased by 42 square units. Find the dimensions of the original rectangle.

Answer 1

For original rectangle

 

Let width = x

Let length = x+7

Let Area = x(x+7) = x² + 7x

 

 

For the new rectangle

 

Let width = 2x

Let length = (x+7)+2 = x+9

 

Area is:

 

2x(x + 9) =  x² + 7x + 42

2x(x + 9) =  x² + 7x + 42

2x² + 18x = x² + 7x + 42

 

x² + 11x - 42 = 0

 

Using quadratic formula:

 

x = (-11 ± √(11² - 4(-42))) / 2

x = (-11 ± √(289)) / 2

x = (-11 ± 17) / 2

 

x = 3      or     x = -14

 

Accept x = 3

 

Original width is 3 units.

Original length is 10 units.