The length of a rectangle is 1 foot less than 4 times its width. How do you find the dimensions of this rectangle if the area is 60 square feet?

1 Answer
Feb 10, 2016

Answer:

Dimensions of rectangle are #4# and #15#.

Explanation:

Assume that the width in feet is #x#. Hence, length of rectangle, which is one less than four times, will be #4x-1#.

As area of a rectangle (which is #60#) is length multiplied by width, it is given by #x*(4x-1)# i.e. #4x^2-x#.

Hence #4x^2-x=60# or

#4x^2-x-60=0#.

As this is a quadratic equation of type #a*x^2+b*x+c#, to factorize this as #a*c# is negative (it is #-240#), we should factorize #240# in two factors whose difference is #1# note that #b=-1#. Hit and trial shows these are 16 and 15.

Hence equation can be written as

#4x^2-16x+15x-60=0# or #4x(x-4)+15(x-4)=0#

or #(4x+5)*(x-4)=0# i.e.

solution is #x=-5/4# or #x=4#.

As width cannot be #-5/4#, it is #4# and length is #(4*4-1)# or #15#.

Hence dimensions of rectangle are #4# and #15#.