the length of a rectangle is 5 more than he width. the area is 594 square meters. what is the length and width

Question

need to know the width and length using application of quadratic equation

Answer 1

Let width = x

Let length = x + 5

Area = 594 m²

 

 

length × width = Area

 

x(x + 5) = 594

 

x² + 5x = 594

 

 

Subtract 594 on both sides of equation.

 

x² + 5x - 594 = 0

 

 

Using the quadratic formula.

 

x = (-5 ± √(25 - 4(-594))) / 2

x = (-5 ± √(2401)) / 2

x = (-5 ± 49) / 2

 

x = (-5 - 49) / 2                and                x = (-5 + 49) / 2

 

x = -27                             and                x = 22

 

 

Since we cannot have a negative value for dimensions, we accept the positive value of x:  x = 22. Substitute this value of x into the dimensions.

 

width = 22 meters

length = 27 meters