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?

1 Answer
Nov 27, 2015

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