Question

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?

Answer 1

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`.