Question

A rectangular carpet and a square carpet have equal areas. The square carpet has a side length of 4 m. The length of the rectangular carpet is 2 m less than three times its width. What are the dimensions of the rectangular carpet?

Answer 1

The dimensions are: `w=8/3m` `l=6m`

Explanation:

If we write the dimensions of rectangular carpet: width - `w`,
height - `h` then we can write, that:

`l=3w-2`

and

`w*(3w-2)=16`

The first equation comes from the sentence: "The length of the rectangular carpet is 2 m less than three times its width." The second comes from the fact that the area of the rectangular and square carpet is equal.

If we expand the equation we get:

`3w^2-2w-16=0`

`Delta=4-4*3*(-16)=4+192=196`

`sqrt(Delta)=14`

`w_1=(2-14)/6<0` We cannot take `w_1` because the dimensions of figures cannot be negative.

`w_2=(2+14)/6=16/6=8/3= 2 2/3`

Now if we know, that `w=8/3` we can calculate

`l=3w-2=8-2=6`

Answer:
The dimensions are: width - `8/3m`, height `6m`