A rectangle is 24 sq ft. The length is 1 foot less than 3 times the width. What is the formula and steps to solve.

Let l, b are the length and width .

l=3w-1.

lw=24 sq ft.

(3w-1)w=24.

3w^2-w=24.

3w^2-w-24=0.

Solve the above quadartic equation by factorisation

-24*3 =-72 =-9*8.

-9+8 =-1 ( matched with middle coeffiicent).

3w^2-9w+8w-24=0.

3w(w-3)+8(w-3)=0.

(w-3)(3w+8)=0.

w=3 or -8/3.

As width can not be negative.

width w=3 ft.

length l=24/w=24/3 =8 ft.