Solve rectangle length using quadratic equation.

Question

Rectangle has an area of 40cm^2. The width is 2cm more then the length. What is the length and width of the rectangle?

Answer 1

The area of a rectangle is length times width.

 

Let length = x

Let width = x + 2

Area = 40 cm²

 

 

Using these variables, set up an equation the represents the area.

 

x(x + 2) = 40

 

 

Solve for x from this equation.

 

x² + 2x = 40

 

 

Subtract 40 on both sides of the equation.

 

x² + 2x - 40 = 0

 

 

Use the quadratic formula to solve for x:

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 1

b = 2

c = -40

 

Plugging in these values into the formula,

 

x = (-2 ± √(4 - 4(-40))) / 2

x = (-2 ± √(164)) / 2

x = (-2 ± 12.806) / 2

 

 

Since we can only have a positive value for dimensions, we accept

 

x = (-2 + 12.806) / 2

x = 5.403

 

 

length = 5.403 cm

width = 7.403 cm