The length of a rectangle is 3m less than twice its width, and the area of the rectangle 65m^2.?

Question

find the dimensions

Answer 1

The length of rectangle is 3mt less than twice its width 

Let the width of rectangle = x mt

Then the length of rectangle = (2x - 3)mt

The formula for area of rectangle = length*width

Area = (2x - 3)m*xm

Area = (2x - 3)*xm^2

Also given area = 65m^2

(2x - 3)*x = 65

Distribute terms using distribution property : a(b - c) = ab - ac

2x(x) - 3(x) = 65

2x^2 - 3x = 65

Subtracting 65 from each side

2x^2 - 3x - 65 = 0

By factorising above equation ,

2x^2 - 13x + 10x - 65 = 0

x( 2x - 13 ) + 5( 2x - 13) = 0

(2x - 13)*(x + 5) = 0

2x - 13 = 0 and x + 5 = 0

x = 13/2 and x =-5 

X value will not be negative, x = 13/2

Substitute x = 13/2 in  ( 2x - 3)

length = 2 (13/2) - 3

length = 13 - 3

length = 10 and width x = 13/2